Naive Bayes - Model.ipynb

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    "# Introduction\n",
    "\n",
    "So today we'll be discussing - the **Naive Bayes Classifier**\n",
    "\n",
    "Why start with Naive Bayes? this classifier is simple, because it's basically just applying \n",
    "Bayes's theorem with class conditional independence assumptions among the features.\n",
    "\n",
    "It still manages to work well finding applications in \n",
    "\n",
    "* Document classification \n",
    "    * Spam filtering\n",
    "    * Context based email routing\n",
    "* Medical Diagnosis\n",
    "\n",
    "etc\n",
    "\n",
    "With some modifications it [can compare][1] in accuracy to complex methods such as SVM when faced with text data, while being computationally much cheaper.\n",
    "\n",
    "Now I will be using the famous iris dataset to show how this classifier works.\n",
    "\n",
    "[1]:http://www.aaai.org/Papers/ICML/2003/ICML03-081.pdf\n"
   ]
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      "   Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm      Species\n",
      "0   1            5.1           3.5            1.4           0.2  Iris-setosa\n",
      "1   2            4.9           3.0            1.4           0.2  Iris-setosa\n",
      "2   3            4.7           3.2            1.3           0.2  Iris-setosa\n",
      "3   4            4.6           3.1            1.5           0.2  Iris-setosa\n",
      "4   5            5.0           3.6            1.4           0.2  Iris-setosa\n",
      "      Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
      "145  146            6.7           3.0            5.2           2.3   \n",
      "146  147            6.3           2.5            5.0           1.9   \n",
      "147  148            6.5           3.0            5.2           2.0   \n",
      "148  149            6.2           3.4            5.4           2.3   \n",
      "149  150            5.9           3.0            5.1           1.8   \n",
      "\n",
      "            Species  \n",
      "145  Iris-virginica  \n",
      "146  Iris-virginica  \n",
      "147  Iris-virginica  \n",
      "148  Iris-virginica  \n",
      "149  Iris-virginica  \n"
     ]
    }
   ],
   "source": [
    "# All needed imports\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split # We need to demarcate the Training and Testing set\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.mlab as mlab\n",
    "import math # for sqrt\n",
    "import scipy.stats # normal distribution\n",
    "from sklearn.preprocessing import normalize\n",
    "import seaborn as sn # Data visualization\n",
    "\n",
    "# Be sure to change this to the correct path for your computer\n",
    "df = pd.read_csv('/home/adityap/Actual Desktop/Ongoing/Machine Learning/Datasets/iris-species/Iris.csv')\n",
    "\n",
    "print(df.head())\n",
    "print(df.tail())\n"
   ]
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   "source": [
    "So the first thing we need to do is familiarize ourselfs with [this dataset](https://archive.ics.uci.edu/ml/datasets/Iris).\n",
    "\n",
    "The Iris flower data set is a famous dataset, The data set contains 3 classes (three species of Iris - Iris setosa, Iris virginica and Iris versicolor) of 50 instances each. Four features were measured from each sample: the length and the width of the sepals and petals, in centimetres.\n",
    "\n",
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/7/78/Petal-sepal.jpg\" alt=\"Petal vs Sepal\" style=\"width: 300px;\"/>\n",
    "\n",
    "So we have,\n",
    "\n",
    "### 3 classes \n",
    "\n",
    "* Class 1 : Iris setosa\n",
    "* Class 2 : Iris virginica\n",
    "* Class 3 : Iris versicolor\n",
    "\n",
    "\n",
    "### 4 features (in cm)\n",
    "\n",
    "* Feature 1 : Sepal Length\n",
    "* Feature 2 : Sepal Width\n",
    "* Feature 3 : Petal Length\n",
    "* Feature 4 : Petal Width\n",
    "\n",
    "                     "
   ]
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    "We have the **independent feature model** (we will derive below),\n",
    "\n",
    "$${\\displaystyle p(C_{k}\\mid x_{1},\\dots ,x_{n})={\\frac {1}{p \\left (\\vec x \\right )}}p(C_{k})\\prod _{i=1}^{n}p(x_{i}\\mid C_{k})}$$\n",
    "\n",
    " \n",
    "## Class Priors\n",
    "\n",
    "So we need to estimate the prior probability, i.e. given a sample, no extra information whats the probability of it being class $C_i$?\n",
    "\n",
    "$$p(C_i)\\ \\ \\  \\forall \\ \\  i \\in \\ [1,2,3]$$\n",
    "\n",
    "This shows what our beliefs are *before* we take the \"evidence\" into account."
   ]
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     "text": [
      "    Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
      "67  68            5.8           2.7            4.1           1.0   \n",
      "34  35            4.9           3.1            1.5           0.1   \n",
      "76  77            6.8           2.8            4.8           1.4   \n",
      "33  34            5.5           4.2            1.4           0.2   \n",
      "84  85            5.4           3.0            4.5           1.5   \n",
      "\n",
      "            Species  \n",
      "67  Iris-versicolor  \n",
      "34      Iris-setosa  \n",
      "76  Iris-versicolor  \n",
      "33      Iris-setosa  \n",
      "84  Iris-versicolor  \n",
      "      Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
      "104  105            6.5           3.0            5.8           2.2   \n",
      "23    24            5.1           3.3            1.7           0.5   \n",
      "37    38            4.9           3.1            1.5           0.1   \n",
      "82    83            5.8           2.7            3.9           1.2   \n",
      "124  125            6.7           3.3            5.7           2.1   \n",
      "\n",
      "             Species  \n",
      "104   Iris-virginica  \n",
      "23       Iris-setosa  \n",
      "37       Iris-setosa  \n",
      "82   Iris-versicolor  \n",
      "124   Iris-virginica  \n",
      "\n",
      "\n",
      "The class priors are \n",
      "\n",
      "0.3333333333333333 0.3333333333333333 0.3333333333333333\n"
     ]
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   "source": [
    "train, test = train_test_split(df, test_size = 0.2)\n",
    "\n",
    "print(test.head())\n",
    "print(train.head())\n",
    "\n",
    "classPriors = {}\n",
    "\n",
    "# Lets go with eqiprobable class priors - more accurate\n",
    "classPriors[1] = 50/150\n",
    "classPriors[2] = 50/150\n",
    "classPriors[3] = 50/150\n",
    "\n",
    "# Alternatively we could try estimating class priors from the training set\n",
    "classCounts = train['Species'].value_counts()\n",
    "totalCount = classCounts[0] + classCounts[1] + classCounts[2]\n",
    "assert (totalCount == 120) # Cause 20% of 150 is test\n",
    "\n",
    "#classPriors[1] = classCounts[1]/totalCount # Iris-setosa\n",
    "#classPriors[2] = classCounts[2]/totalCount # Iris-virginica\n",
    "#classPriors[3] = classCounts[0]/totalCount # Iris-versicolor\n",
    "\n",
    "print(\"\\n\\nThe class priors are \\n\")\n",
    "print( str(classPriors[1])+\" \"+str(classPriors[2])+\" \"+str(classPriors[3]) )\n",
    "\n",
    "assert ( classPriors[1]+classPriors[2]+classPriors[3] == 1)"
   ]
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    "### Event Model\n",
    "\n",
    "We need to make some assumptions on how the features are distibuted. What are the values of the features for a given class likely to be?\n",
    "\n",
    "As we are dealing with continous data **let's assume the data is normally distributed**. Note that in some cases we can't make such assumptions then we can try non parametric models.\n",
    "\n",
    "There are Multinomial Naive Bayes (bag of words), Bernoulli Naive Bayes which are popular when we have features taking on discrete values, used in document classification.\n",
    "\n",
    "So today we will be building a **Gaussian** Naive Bayes classifier.\n",
    "\n",
    "So the probability density function will be,\n",
    "\n",
    "$$\\Large {\\displaystyle f(x=x_0\\mid C_i)={\\frac {1}{\\sqrt {2\\pi \\sigma _{c}^{2}}}}\\,e^{-{\\frac {(x_0-\\mu _{c})^{2}}{2\\sigma _{c}^{2}}}}} $$\n",
    "\n",
    "-----\n",
    "\n",
    "\n",
    "So in the orginal bayes equation,\n",
    "\n",
    "$$ p(C_{k} \\ | \\ \\mathbf {x}) = \\frac {p(C_{k})\\ p(\\mathbf {x} \\mid C_{k})}{p(\\mathbf {x})} = \\frac {p(\\mathbf {x} , C_{k})}{p(\\mathbf {x})}$$\n",
    "\n",
    "Or in words this is,\n",
    "\n",
    "$${\\displaystyle {\\mbox{posterior}}={\\frac {{\\mbox{prior}}\\times {\\mbox{likelihood}}}{\\mbox{evidence}}}\\,}$$\n",
    "\n",
    "So now we will be tackling on estimating the **Likelyhood**!\n",
    "\n",
    "\n",
    "## Likelyhood probability density function\n",
    "\n",
    "Because we are talking about continous random variables, what we are going to estimate is a pdf.\n",
    "\n",
    "Due to the assumption that **each feature is conditionally independent of each other given the class**, so the joint probability model will be,\n",
    "\n",
    "$$p(\\mathbf {x}, C_{k}) = p(C_{k})\\prod _{i=1}^{n}p(x_{i}\\mid C_{k})$$\n",
    "\n",
    "Which means,\n",
    "\n",
    "$$p(\\mathbf {x} \\mid C_{k}) = \\prod _{i=1}^{n}p(x_{i}\\mid C_{k}) $$\n",
    "\n",
    "$$p(\\mathbf {x} \\mid C_{k}) \\propto \\prod _{i=1}^{n}f(x_{i}\\mid C_{k}) $$\n",
    "\n",
    "The actual probability should be something like \n",
    "\n",
    "$${\\displaystyle p(x = x_{0} \\ | \\ C_{i})=\\int _{x_{0}-\\epsilon }^{x_{0}+\\epsilon }f(x \\ | \\ \\;\\mu _{i},\\sigma _{i}^{2})dx}$$\n",
    "\n",
    "Where the probability density of the normal (gaussian) distribution is,\n",
    "\n",
    "$${ \\Large \\displaystyle {\\displaystyle f(x \\; \\ | \\; \\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\sigma ^{2}\\pi }}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}}} $$\n",
    "\n",
    "Please note that the density of a continuous random variable is not a probability, in a similar way to instantaneous velocity not being a distance."
   ]
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     "text": [
      "      Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm  \\\n",
      "100  101            6.3           3.3            6.0           2.5   \n",
      "101  102            5.8           2.7            5.1           1.9   \n",
      "102  103            7.1           3.0            5.9           2.1   \n",
      "103  104            6.3           2.9            5.6           1.8   \n",
      "104  105            6.5           3.0            5.8           2.2   \n",
      "\n",
      "            Species  \n",
      "100  Iris-virginica  \n",
      "101  Iris-virginica  \n",
      "102  Iris-virginica  \n",
      "103  Iris-virginica  \n",
      "104  Iris-virginica  \n",
      "Id               25.500\n",
      "SepalLengthCm     5.006\n",
      "SepalWidthCm      3.418\n",
      "PetalLengthCm     1.464\n",
      "PetalWidthCm      0.244\n",
      "dtype: float64\n"
     ]
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   "source": [
    "dfClasses = {}\n",
    "means = {}\n",
    "variances = {}\n",
    "\n",
    "# Seperate training set w.r.t class labels\n",
    "dfClasses[\"Iris-setosa\"] = df.loc[df['Species'] == \"Iris-setosa\"]\n",
    "dfClasses[\"Iris-virginica\"] = df.loc[df['Species'] == \"Iris-virginica\"]\n",
    "dfClasses[\"Iris-versicolor\"] = df.loc[df['Species'] == \"Iris-versicolor\"]\n",
    "\n",
    "print(dfClasses[\"Iris-virginica\"].head()) # Try different classes\n",
    "\n",
    "# find mu_i and var_i which are parameters for the Gaussian Event Model\n",
    "means[1] = dfClasses[\"Iris-setosa\"].mean()\n",
    "variances[1] = dfClasses[\"Iris-setosa\"].var()\n",
    "\n",
    "means[2] = dfClasses[\"Iris-virginica\"].mean()\n",
    "variances[2] = dfClasses[\"Iris-virginica\"].var()\n",
    "\n",
    "means[3] = dfClasses[\"Iris-versicolor\"].mean()\n",
    "variances[3] = dfClasses[\"Iris-versicolor\"].var()\n",
    "\n",
    "# Feature means for Class 1, With one more indexing I can specify my desired feature\n",
    "print(means[1]) \n",
    "\n",
    "# variances[classNo][featureNo]"
   ]
  },
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   "source": [
    "### Feature 1 : Sepal length "
   ]
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zbdu2tG3btlz7XnTRRUGti0hN5PWazFqXLqeL3SYsDOrVy+bQIQVrIi69G0RE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CJfB8YA/SQNLbvWKfuHAov6qi29mVbm/ehO0knkyM/5wKiIeGIFh6zt3inb9Rrsqz231v8srKoy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\nZmZm1sKcrJmZmZm1MCdrZmZmZi3sf71oeudDtGRtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccb00b4ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# I'll now plot the gaussian curves, \n",
    "# we can see the probability distribution of each feature given a particular class.\n",
    "\n",
    "# Length in cm\n",
    "x = np.linspace(-5, 10, 1000)\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(10, 8)\n",
    "\n",
    "plt.title('Feature 1\\'s Likelyhood pdf vs Sepal length in cm', size='xx-large')\n",
    "plt.xlabel('Sepal Length (cm)')\n",
    "plt.ylabel('PDF of likelyhood')\n",
    "\n",
    "# Note variance is the square of the standard deviation, here sd is the required input\n",
    "plt.plot(x,mlab.normpdf(x, means[1][1], math.sqrt(variances[1][1]) ), c = 'b', label = 'Iris setosa')\n",
    "plt.plot(x,mlab.normpdf(x, means[2][1], math.sqrt(variances[2][1]) ), c = 'r', label = 'Iris virginica')\n",
    "plt.plot(x,mlab.normpdf(x, means[3][1], math.sqrt(variances[3][1]) ), c = 'g', label = 'Iris versicolor')\n",
    "\n",
    "plt.legend(loc=2) # 2 => leftTop ; 1 => rightTop\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that pdf can be greater than 1.0, the probability in this case is the **area under this graph**.\n",
    "\n",
    "### Feature 2 :  Sepal Width "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SEhKYOnUq55133ll7zFGjRtG3b19iY2Pr7ZoDBw6kffv2tHftNxSgO+64g4KC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Dd27WFg89wlQ5rAj4CPGWNeYq29DtKrGlwAPMDMB08zuBhvJYtbgLOarJsvLVf3vzFmEq/7s+k+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\nFXOyZmZmZlbF/gapX7MPaVl3NgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabedfcc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Then Sepal Width (feature 2) for all 3 classes\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(10, 8)\n",
    "\n",
    "plt.plot(x,mlab.normpdf(x, means[1][2], math.sqrt(variances[1][2]) ), c = 'b', label = 'Iris setosa')\n",
    "plt.plot(x,mlab.normpdf(x, means[2][2], math.sqrt(variances[2][2]) ), c = 'r', label = 'Iris virginica')\n",
    "plt.plot(x,mlab.normpdf(x, means[3][2], math.sqrt(variances[3][2]) ), c = 'g', label = 'Iris versicolor')\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlabel('Sepal Width (cm)')\n",
    "plt.ylabel('PDF of likelyhood')\n",
    "plt.title('Feature 2\\'s Likelyhood pdf vs Sepal Width in cm')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature 3 :  Petal Length "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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raNu2LYsWLeLYsWPllkCDxbZ161YATjnllFLbnnbaaaxcuTLiYyYkJJCUlERB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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabee7ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Then Petal Length (feature 3) for all 3 classes\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(10, 8)\n",
    "\n",
    "plt.plot(x,mlab.normpdf(x, means[1][3], math.sqrt(variances[1][3]) ), c = 'b', label = 'Iris setosa')\n",
    "plt.plot(x,mlab.normpdf(x, means[2][3], math.sqrt(variances[2][3]) ), c = 'r', label = 'Iris virginica')\n",
    "plt.plot(x,mlab.normpdf(x, means[3][3], math.sqrt(variances[3][3]) ), c = 'g', label = 'Iris versicolor')\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlabel('Petal Length (cm)')\n",
    "plt.ylabel('PDF of likelyhood')\n",
    "plt.title('Feature 3\\'s Likelyhood pdf vs Petal Length in cm')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Feature 4 : Petal Width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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j6NChbN68mZ49e3LmmWeybt06pk+fzjfffMPo0U5XywceeIDPPvuM3r17c8UV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabd954e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Then Petal Width (feature 4) for all 3 classes\n",
    "\n",
    "fig = plt.figure()\n",
    "fig.set_size_inches(10, 8)\n",
    "\n",
    "plt.plot(x,mlab.normpdf(x, means[1][4], math.sqrt(variances[1][4]) ), c = 'b', label = 'Iris setosa')\n",
    "plt.plot(x,mlab.normpdf(x, means[2][4], math.sqrt(variances[2][4]) ), c = 'r', label = 'Iris virginica')\n",
    "plt.plot(x,mlab.normpdf(x, means[3][4], math.sqrt(variances[3][4]) ), c = 'g', label = 'Iris versicolor')\n",
    "\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlabel('Petal Width (cm)')\n",
    "plt.ylabel('PDF of likelyhood')\n",
    "plt.title('Feature 4\\'s Likelyhood pdf vs Petal Width in cm')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior Probability\n",
    "\n",
    "Now lets try to compute the posterior probability for the training set, then move on to the testing set\n",
    "\n",
    "So we will get 3 posterier probabilities, one for each value of $i$\n",
    "\n",
    "$$p(C_k \\ | \\; \\mathbf {x}) \\propto p(C_{k})\\prod _{i=1}^{n}f(x_{i}\\mid C_{k}) $$\n",
    "\n",
    "We can calculate $p(C_k \\ | \\; \\mathbf {x})$ by normalizing these 3 values, because each sample has to be in one of these 3 classes.\n",
    "\n",
    "$$\\sum_{k=1}^3 p(C_k \\ | \\; \\mathbf {x}) = 1$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.50981390027\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# return f(x_i | C_k) \n",
    "# i.e. the probability density of getting \"x\" in feature i's prob distribution given class k\n",
    "def pdfFeatureGivenClass(x,i,k):\n",
    "    ourCalc = (1/math.sqrt(2*math.pi*variances[k][i]))*math.exp( (-(x-means[k][i])**2) / (2*variances[k][i]))\n",
    "    scipyCalc = scipy.stats.norm( means[k][i], math.sqrt(variances[k][i]) ).pdf(x)\n",
    "    \n",
    "    # You might see around 10^(-16)\n",
    "    #print(\"error in our calculation : \"+str(scipyCalc-ourCalc))\n",
    "    return(scipyCalc)\n",
    "\n",
    "\n",
    "print(pdfFeatureGivenClass(0.1,4,1)) # Try different values\n",
    "\n",
    "# Given a string - class name, return class no\n",
    "def labelofClass(x):\n",
    "    return {\n",
    "        'Iris-setosa': 1,\n",
    "        'Iris-virginica': 2,\n",
    "        'Iris-versicolor': 3,\n",
    "    }.get(x, -1)    # -1 is default if x not found\n",
    "\n",
    "labelofClass('Iris-setosa') # Just testing it\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "For the sample in the 104th row with id : 105 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.5\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.8\n",
      "Petal Width : 2.2\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.05350791699e-212\n",
      "\n",
      " \t the posterior prob is propotional to 3.01783597233e-212\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.595019621514\n",
      "\n",
      " \t the posterior prob is propotional to 0.198339873838\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.88941667913e-07\n",
      "\n",
      " \t the posterior prob is propotional to 6.29805559709e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.017835972331559e-212, 0.19833987383813526, 6.2980555970889229e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.52154731e-211   9.99999682e-001   3.17538449e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 23th row with id : 24 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 1.7\n",
      "Petal Width : 0.5\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.21372603285\n",
      "\n",
      " \t the posterior prob is propotional to 0.0712420109499\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.65323199908e-19\n",
      "\n",
      " \t the posterior prob is propotional to 5.51077333027e-20\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 6.36460819085e-12\n",
      "\n",
      " \t the posterior prob is propotional to 2.12153606362e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.071242010949855022, 5.5107733302739614e-20, 2.1215360636166139e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   7.73528604e-19   2.97792838e-11]]\n",
      "\n",
      "\n",
      "For the sample in the 37th row with id : 38 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.71637515617\n",
      "\n",
      " \t the posterior prob is propotional to 0.905458385392\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.20596040171e-25\n",
      "\n",
      " \t the posterior prob is propotional to 3.06865346724e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.87886314321e-17\n",
      "\n",
      " \t the posterior prob is propotional to 6.26287714402e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.90545838539161227, 3.0686534672378497e-25, 6.2628771440215517e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.38906074e-25   6.91680285e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 82th row with id : 83 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 3.9\n",
      "Petal Width : 1.2\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.1631107317e-61\n",
      "\n",
      " \t the posterior prob is propotional to 3.87703577233e-62\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.24478640065e-05\n",
      "\n",
      " \t the posterior prob is propotional to 1.08159546688e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.965107002632\n",
      "\n",
      " \t the posterior prob is propotional to 0.321702334211\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.8770357723326964e-62, 1.0815954668842589e-05, 0.32170233421072458])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.20512194e-61   3.36198712e-05   9.99966380e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 124th row with id : 125 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 5.7\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.9346127797e-199\n",
      "\n",
      " \t the posterior prob is propotional to 9.782042599e-200\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.447813737972\n",
      "\n",
      " \t the posterior prob is propotional to 0.149271245991\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.82387835511e-07\n",
      "\n",
      " \t the posterior prob is propotional to 1.94129278504e-07\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([9.7820425990007666e-200, 0.14927124599074662, 1.941292785037309e-07])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.55319101e-199   9.99998699e-001   1.30051186e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 117th row with id : 118 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.7\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 6.7\n",
      "Petal Width : 2.2\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.20381956335e-282\n",
      "\n",
      " \t the posterior prob is propotional to 4.01273187782e-283\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000624900754757\n",
      "\n",
      " \t the posterior prob is propotional to 0.000208300251586\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.79533738564e-15\n",
      "\n",
      " \t the posterior prob is propotional to 5.98445795215e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.012731877824434e-283, 0.00020830025158564237, 5.9844579521471784e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.92641720e-279   1.00000000e+000   2.87299603e-012]]\n",
      "\n",
      "\n",
      "For the sample in the 140th row with id : 141 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 5.6\n",
      "Petal Width : 2.4\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.33206066114e-216\n",
      "\n",
      " \t the posterior prob is propotional to 1.44402022038e-216\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.293034239932\n",
      "\n",
      " \t the posterior prob is propotional to 0.0976780799775\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.18492781684e-09\n",
      "\n",
      " \t the posterior prob is propotional to 7.28309272279e-10\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.4440202203806553e-216, 0.09767807997749986, 7.2830927227914015e-10])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.47834623e-215   9.99999993e-001   7.45622014e-009]]\n",
      "\n",
      "\n",
      "For the sample in the 56th row with id : 57 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 4.7\n",
      "Petal Width : 1.6\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 6.1817184516e-113\n",
      "\n",
      " \t the posterior prob is propotional to 2.0605728172e-113\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0402479323814\n",
      "\n",
      " \t the posterior prob is propotional to 0.0134159774605\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0778682980068\n",
      "\n",
      " \t the posterior prob is propotional to 0.0259560993356\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.0605728172010286e-113, 0.013415977460473592, 0.0259560993356154])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.23358935e-112   3.40748534e-001   6.59251466e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 139th row with id : 140 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 5.4\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.83058287697e-183\n",
      "\n",
      " \t the posterior prob is propotional to 1.94352762566e-183\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.621505233303\n",
      "\n",
      " \t the posterior prob is propotional to 0.207168411101\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 4.20707593595e-06\n",
      "\n",
      " \t the posterior prob is propotional to 1.40235864532e-06\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.9435276256559704e-183, 0.20716841110109679, 1.4023586453156006e-06])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  9.38132633e-183   9.99993231e-001   6.76912636e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 52th row with id : 53 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 4.9\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.24387873141e-121\n",
      "\n",
      " \t the posterior prob is propotional to 1.4146262438e-121\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.053229140093\n",
      "\n",
      " \t the posterior prob is propotional to 0.0177430466977\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0454576280084\n",
      "\n",
      " \t the posterior prob is propotional to 0.0151525426695\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.4146262438024904e-121, 0.017743046697659214, 0.015152542669481371])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.30035233e-120   5.39374641e-001   4.60625359e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 72th row with id : 73 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 4.9\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.2694235181e-119\n",
      "\n",
      " \t the posterior prob is propotional to 2.4231411727e-119\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0198579792751\n",
      "\n",
      " \t the posterior prob is propotional to 0.00661932642504\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.243444935587\n",
      "\n",
      " \t the posterior prob is propotional to 0.0811483118623\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.423141172698784e-119, 0.0066193264250392746, 0.0811483118622843])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.76085949e-118   7.54187597e-002   9.24581240e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 92th row with id : 93 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.6\n",
      "Petal Length : 4.0\n",
      "Petal Width : 1.2\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.77709829924e-65\n",
      "\n",
      " \t the posterior prob is propotional to 5.92366099747e-66\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 4.02079677349e-05\n",
      "\n",
      " \t the posterior prob is propotional to 1.34026559116e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.983150158508\n",
      "\n",
      " \t the posterior prob is propotional to 0.327716719503\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.923660997465596e-66, 1.3402655911637795e-05, 0.32771671950256392])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.80748140e-65   4.08954045e-05   9.99959105e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 93th row with id : 94 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 2.3\n",
      "Petal Length : 3.3\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.06006696484e-36\n",
      "\n",
      " \t the posterior prob is propotional to 3.53355654947e-37\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.17169108729e-10\n",
      "\n",
      " \t the posterior prob is propotional to 3.05723036243e-10\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00337658272841\n",
      "\n",
      " \t the posterior prob is propotional to 0.00112552757614\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.533556549469772e-37, 3.0572303624302771e-10, 0.0011255275761375785])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.13946603e-34   2.71626355e-07   9.99999728e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 113th row with id : 114 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 5.0\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.92026673888e-150\n",
      "\n",
      " \t the posterior prob is propotional to 9.73422246294e-151\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0630022034824\n",
      "\n",
      " \t the posterior prob is propotional to 0.0210007344941\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.000909731612098\n",
      "\n",
      " \t the posterior prob is propotional to 0.000303243870699\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([9.7342224629377511e-151, 0.02100073449411698, 0.00030324387069923848])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.56920407e-149   9.85765857e-001   1.42341428e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 130th row with id : 131 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.4\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 6.1\n",
      "Petal Width : 1.9\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.88585774659e-217\n",
      "\n",
      " \t the posterior prob is propotional to 1.29528591553e-217\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.171397353427\n",
      "\n",
      " \t the posterior prob is propotional to 0.0571324511425\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.08161785513e-07\n",
      "\n",
      " \t the posterior prob is propotional to 6.93872618376e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.295285915531443e-217, 0.05713245114249553, 6.9387261837558915e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.26716046e-216   9.99998786e-001   1.21449677e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 87th row with id : 88 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.3\n",
      "Petal Length : 4.4\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.2907598362e-88\n",
      "\n",
      " \t the posterior prob is propotional to 3.0969199454e-88\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000284891903084\n",
      "\n",
      " \t the posterior prob is propotional to 9.49639676947e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.405423592828\n",
      "\n",
      " \t the posterior prob is propotional to 0.135141197609\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.0969199453997332e-88, 9.4963967694723945e-05, 0.13514119760936427])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.29000876e-87   7.02208393e-04   9.99297792e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 0th row with id : 1 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.21034920576\n",
      "\n",
      " \t the posterior prob is propotional to 2.73678306859\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.8025267716e-24\n",
      "\n",
      " \t the posterior prob is propotional to 6.00842257201e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.49672785999e-17\n",
      "\n",
      " \t the posterior prob is propotional to 8.32242619997e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.7367830685875512, 6.0084225720110313e-25, 8.3224261999681391e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.19543253e-25   3.04095209e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 80th row with id : 81 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 2.4\n",
      "Petal Length : 3.8\n",
      "Petal Width : 1.1\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 6.71702260746e-55\n",
      "\n",
      " \t the posterior prob is propotional to 2.23900753582e-55\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 8.52632040396e-07\n",
      "\n",
      " \t the posterior prob is propotional to 2.84210680132e-07\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.189467068714\n",
      "\n",
      " \t the posterior prob is propotional to 0.0631556895714\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.2390075358187319e-55, 2.8421068013185831e-07, 0.063155689571354645])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.54520309e-54   4.50013931e-06   9.99995500e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 126th row with id : 127 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.2\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.8\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.55765999123e-129\n",
      "\n",
      " \t the posterior prob is propotional to 2.85255333041e-129\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.164760081178\n",
      "\n",
      " \t the posterior prob is propotional to 0.0549200270593\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.042947830665\n",
      "\n",
      " \t the posterior prob is propotional to 0.014315943555\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.8525533304091725e-129, 0.054920027059268246, 0.01431594355500289])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.12004527e-128   7.93229684e-001   2.06770316e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 60th row with id : 61 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 2.0\n",
      "Petal Length : 3.5\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.00381603303e-43\n",
      "\n",
      " \t the posterior prob is propotional to 6.67938677677e-44\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.49855263851e-10\n",
      "\n",
      " \t the posterior prob is propotional to 1.16618421284e-10\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00111280089415\n",
      "\n",
      " \t the posterior prob is propotional to 0.000370933631384\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([6.6793867767747988e-44, 1.1661842128367975e-10, 0.00037093363138407604])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.80069536e-40   3.14391510e-07   9.99999686e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 29th row with id : 30 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.7\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.99273132282\n",
      "\n",
      " \t the posterior prob is propotional to 1.33091044094\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.43613080206e-23\n",
      "\n",
      " \t the posterior prob is propotional to 4.78710267352e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.75802217888e-16\n",
      "\n",
      " \t the posterior prob is propotional to 1.25267405963e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.3309104409386248, 4.7871026735230419e-24, 1.2526740596264665e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.59686311e-24   9.41215893e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 136th row with id : 137 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 5.6\n",
      "Petal Width : 2.4\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.5212084648e-214\n",
      "\n",
      " \t the posterior prob is propotional to 2.50706948827e-214\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.121160005025\n",
      "\n",
      " \t the posterior prob is propotional to 0.0403866683417\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.18050514136e-09\n",
      "\n",
      " \t the posterior prob is propotional to 3.93501713788e-10\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.5070694882677783e-214, 0.040386668341720555, 3.9350171378811436e-10])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.20766596e-213   9.99999990e-001   9.74335656e-009]]\n",
      "\n",
      "\n",
      "For the sample in the 42th row with id : 43 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.4\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.1548309306\n",
      "\n",
      " \t the posterior prob is propotional to 0.384943643534\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 5.57008208711e-26\n",
      "\n",
      " \t the posterior prob is propotional to 1.85669402904e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.73462451152e-18\n",
      "\n",
      " \t the posterior prob is propotional to 5.78208170508e-19\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.38494364353417265, 1.8566940290381771e-26, 5.7820817050773145e-19])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   4.82328793e-26   1.50205928e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 64th row with id : 65 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 3.6\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.02881483508e-54\n",
      "\n",
      " \t the posterior prob is propotional to 3.42938278359e-55\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.3858238902e-05\n",
      "\n",
      " \t the posterior prob is propotional to 4.61941296735e-06\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.462020976986\n",
      "\n",
      " \t the posterior prob is propotional to 0.154006992329\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.4293827835910313e-55, 4.6194129673451781e-06, 0.15400699232876125])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.22670404e-54   2.99939265e-05   9.99970006e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 120th row with id : 121 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.9\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 5.7\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.40838601329e-215\n",
      "\n",
      " \t the posterior prob is propotional to 8.02795337764e-216\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.331474673519\n",
      "\n",
      " \t the posterior prob is propotional to 0.11049155784\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.67539563625e-09\n",
      "\n",
      " \t the posterior prob is propotional to 1.89179854542e-09\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.0279533776376119e-216, 0.11049155783974565, 1.8917985454166861e-09])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.26567115e-215   9.99999983e-001   1.71216566e-008]]\n",
      "\n",
      "\n",
      "For the sample in the 61th row with id : 62 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.9\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.2\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.5650933977e-85\n",
      "\n",
      " \t the posterior prob is propotional to 1.1883644659e-85\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00359643641504\n",
      "\n",
      " \t the posterior prob is propotional to 0.00119881213835\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.864349613634\n",
      "\n",
      " \t the posterior prob is propotional to 0.288116537878\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1883644658988247e-85, 0.0011988121383476932, 0.28811653787784913])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.10750576e-85   4.14361747e-03   9.95856383e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 15th row with id : 16 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 4.4\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0178965072378\n",
      "\n",
      " \t the posterior prob is propotional to 0.00596550241261\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 8.43018202175e-25\n",
      "\n",
      " \t the posterior prob is propotional to 2.81006067392e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.17275851829e-18\n",
      "\n",
      " \t the posterior prob is propotional to 3.90919506096e-19\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.0059655024126096159, 2.8100606739182022e-25, 3.9091950609607045e-19])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   4.71051804e-23   6.55300223e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 125th row with id : 126 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.2\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 6.0\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.38278095495e-202\n",
      "\n",
      " \t the posterior prob is propotional to 7.94260318317e-203\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.20568458016\n",
      "\n",
      " \t the posterior prob is propotional to 0.0685615267201\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.95566526129e-06\n",
      "\n",
      " \t the posterior prob is propotional to 6.5188842043e-07\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.9426031831742602e-203, 0.068561526720071181, 6.5188842042953844e-07])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.15845257e-201   9.99990492e-001   9.50798871e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 47th row with id : 48 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.6\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.80801510674\n",
      "\n",
      " \t the posterior prob is propotional to 1.26933836891\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 6.21633906627e-25\n",
      "\n",
      " \t the posterior prob is propotional to 2.07211302209e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.90406136991e-17\n",
      "\n",
      " \t the posterior prob is propotional to 6.34687123303e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.2693383689125506, 2.0721130220883562e-25, 6.3468712330272303e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.63243551e-25   5.00014132e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 54th row with id : 55 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.5\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.6\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 6.26372014582e-105\n",
      "\n",
      " \t the posterior prob is propotional to 2.08790671527e-105\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0251851583784\n",
      "\n",
      " \t the posterior prob is propotional to 0.00839505279279\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.481975182323\n",
      "\n",
      " \t the posterior prob is propotional to 0.160658394108\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.0879067152717104e-105, 0.0083950527927887809, 0.16065839410782859])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.23505717e-104   4.96591637e-002   9.50340836e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 121th row with id : 122 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.9\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.56130927863e-144\n",
      "\n",
      " \t the posterior prob is propotional to 8.53769759542e-145\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.104388850364\n",
      "\n",
      " \t the posterior prob is propotional to 0.0347962834546\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00160982084244\n",
      "\n",
      " \t the posterior prob is propotional to 0.00053660694748\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.5376975954174699e-145, 0.03479628345456727, 0.00053660694747985089])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.41635980e-143   9.84812821e-001   1.51871795e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 142th row with id : 143 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 5.1\n",
      "Petal Width : 1.9\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.28739885769e-149\n",
      "\n",
      " \t the posterior prob is propotional to 3.09579961923e-149\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.169640740284\n",
      "\n",
      " \t the posterior prob is propotional to 0.0565469134282\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00475114316053\n",
      "\n",
      " \t the posterior prob is propotional to 0.00158371438684\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.0957996192288027e-149, 0.056546913428150186, 0.001583714386843839])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.32559123e-148   9.72755939e-001   2.72440613e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 24th row with id : 25 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.8\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.9\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.333921974058\n",
      "\n",
      " \t the posterior prob is propotional to 0.111307324686\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 5.11290283041e-22\n",
      "\n",
      " \t the posterior prob is propotional to 1.70430094347e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 6.049923314e-15\n",
      "\n",
      " \t the posterior prob is propotional to 2.01664110467e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.11130732468583639, 1.7043009434693556e-22, 2.0166411046657168e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.53116693e-21   1.81177754e-14]]\n",
      "\n",
      "\n",
      "For the sample in the 48th row with id : 49 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.3\n",
      "Sepal Width : 3.7\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.89834539947\n",
      "\n",
      " \t the posterior prob is propotional to 1.63278179982\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 4.13164205324e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.37721401775e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.86971744924e-17\n",
      "\n",
      " \t the posterior prob is propotional to 9.56572483081e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.6327817998232448, 1.3772140177469809e-24, 9.565724830814302e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   8.43477076e-25   5.85854450e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 110th row with id : 111 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.5\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 5.1\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.64673827073e-157\n",
      "\n",
      " \t the posterior prob is propotional to 8.82246090244e-158\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.449476018992\n",
      "\n",
      " \t the posterior prob is propotional to 0.149825339664\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.000220136855985\n",
      "\n",
      " \t the posterior prob is propotional to 7.33789519951e-05\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.822460902442744e-158, 0.14982533966395017, 7.3378951995096403e-05])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.88561462e-157   9.99510476e-001   4.89523544e-004]]\n",
      "\n",
      "\n",
      "For the sample in the 88th row with id : 89 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.1\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.76535660568e-72\n",
      "\n",
      " \t the posterior prob is propotional to 2.92178553523e-72\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000231804936505\n",
      "\n",
      " \t the posterior prob is propotional to 7.72683121682e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.973780335474\n",
      "\n",
      " \t the posterior prob is propotional to 0.324593445158\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.9217855352282963e-72, 7.7268312168214394e-05, 0.32459344515812544])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.99922726e-72   2.37989782e-04   9.99762010e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 123th row with id : 124 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 4.9\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.58968239377e-134\n",
      "\n",
      " \t the posterior prob is propotional to 8.6322746459e-135\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.181849982463\n",
      "\n",
      " \t the posterior prob is propotional to 0.060616660821\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0286350487236\n",
      "\n",
      " \t the posterior prob is propotional to 0.00954501624119\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.6322746458963592e-135, 0.060616660820998841, 0.0095450162411850996])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.23034041e-133   8.63956840e-001   1.36043160e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 4th row with id : 5 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.6\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.76701835212\n",
      "\n",
      " \t the posterior prob is propotional to 2.58900611737\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.08216641461e-25\n",
      "\n",
      " \t the posterior prob is propotional to 2.3607221382e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 8.10839493592e-18\n",
      "\n",
      " \t the posterior prob is propotional to 2.70279831197e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.58900611737395, 2.3607221382040698e-25, 2.7027983119749901e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   9.11825632e-26   1.04395208e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 81th row with id : 82 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 2.4\n",
      "Petal Length : 3.7\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.48011269705e-48\n",
      "\n",
      " \t the posterior prob is propotional to 4.93370899017e-49\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.2939107218e-07\n",
      "\n",
      " \t the posterior prob is propotional to 4.31303573933e-08\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0742532989095\n",
      "\n",
      " \t the posterior prob is propotional to 0.0247510996365\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.9337089901689606e-49, 4.3130357393322172e-08, 0.02475109963649829])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.99332574e-47   1.74256024e-06   9.99998257e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 75th row with id : 76 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.6\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.4\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.63924336877e-92\n",
      "\n",
      " \t the posterior prob is propotional to 2.54641445626e-92\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00684549088847\n",
      "\n",
      " \t the posterior prob is propotional to 0.00228183029616\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.501628632301\n",
      "\n",
      " \t the posterior prob is propotional to 0.1672095441\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.546414456255992e-92, 0.0022818302961559534, 0.16720954410021538])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.50238587e-91   1.34628107e-02   9.86537189e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 97th row with id : 98 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.2\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.3\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.08206431801e-81\n",
      "\n",
      " \t the posterior prob is propotional to 3.60688106005e-82\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00152766128213\n",
      "\n",
      " \t the posterior prob is propotional to 0.000509220427376\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.33862551204\n",
      "\n",
      " \t the posterior prob is propotional to 0.446208504015\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.6068810600483411e-82, 0.00050922042737575491, 0.44620850401497886])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.07418390e-82   1.13991543e-03   9.98860085e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 106th row with id : 107 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.7\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.5606074579e-107\n",
      "\n",
      " \t the posterior prob is propotional to 5.20202485966e-108\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00065595809763\n",
      "\n",
      " \t the posterior prob is propotional to 0.00021865269921\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.022761461737\n",
      "\n",
      " \t the posterior prob is propotional to 0.00758715391234\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.202024859657319e-108, 0.0002186526992101611, 0.0075871539123448274])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.66430149e-106   2.80115445e-002   9.71988456e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 17th row with id : 18 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.79274951636\n",
      "\n",
      " \t the posterior prob is propotional to 2.59758317212\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.89842083389e-23\n",
      "\n",
      " \t the posterior prob is propotional to 6.32806944631e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.9113525865e-16\n",
      "\n",
      " \t the posterior prob is propotional to 1.3037841955e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.5975831721194815, 6.3280694463145019e-24, 1.3037841954989732e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.43613737e-24   5.01922021e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 144th row with id : 145 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 5.7\n",
      "Petal Width : 2.5\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.47335871799e-230\n",
      "\n",
      " \t the posterior prob is propotional to 8.24452905996e-231\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.104734198984\n",
      "\n",
      " \t the posterior prob is propotional to 0.0349113996613\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.74470174538e-11\n",
      "\n",
      " \t the posterior prob is propotional to 9.14900581792e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.2445290599622539e-231, 0.034911399661339243, 9.1490058179226096e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.36155787e-229   1.00000000e+000   2.62063564e-010]]\n",
      "\n",
      "\n",
      "For the sample in the 118th row with id : 119 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.7\n",
      "Sepal Width : 2.6\n",
      "Petal Length : 6.9\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.10628640683e-306\n",
      "\n",
      " \t the posterior prob is propotional to 7.02095468944e-307\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00277598499986\n",
      "\n",
      " \t the posterior prob is propotional to 0.000925328333286\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.19646116001e-15\n",
      "\n",
      " \t the posterior prob is propotional to 1.06548705334e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.0209546894371995e-307, 0.00092532833328647329, 1.065487053335556e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.58752806e-304   1.00000000e+000   1.15146918e-012]]\n",
      "\n",
      "\n",
      "For the sample in the 143th row with id : 144 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.8\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 5.9\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.28485501965e-227\n",
      "\n",
      " \t the posterior prob is propotional to 1.09495167322e-227\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.300517157571\n",
      "\n",
      " \t the posterior prob is propotional to 0.100172385857\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.9825163509e-09\n",
      "\n",
      " \t the posterior prob is propotional to 6.60838783634e-10\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.0949516732163612e-227, 0.10017238585713896, 6.6083878363366702e-10])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.09306737e-226   9.99999993e-001   6.59701547e-009]]\n",
      "\n",
      "\n",
      "For the sample in the 11th row with id : 12 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.8\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.77230067294\n",
      "\n",
      " \t the posterior prob is propotional to 1.92410022431\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.20878872769e-23\n",
      "\n",
      " \t the posterior prob is propotional to 4.02929575895e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.99881949228e-16\n",
      "\n",
      " \t the posterior prob is propotional to 6.66273164093e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.9241002243149841, 4.0292957589527576e-24, 6.6627316409274369e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.09411948e-24   3.46277785e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 58th row with id : 59 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.6\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.6\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.45519321237e-96\n",
      "\n",
      " \t the posterior prob is propotional to 4.85064404123e-97\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00544730097297\n",
      "\n",
      " \t the posterior prob is propotional to 0.00181576699099\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.515251035974\n",
      "\n",
      " \t the posterior prob is propotional to 0.171750345325\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.850644041225022e-97, 0.0018157669909907039, 0.17175034532470873])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.79469533e-96   1.04615294e-02   9.89538471e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 90th row with id : 91 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 2.6\n",
      "Petal Length : 4.4\n",
      "Petal Width : 1.2\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.37340166464e-80\n",
      "\n",
      " \t the posterior prob is propotional to 4.5780055488e-81\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000118348743836\n",
      "\n",
      " \t the posterior prob is propotional to 3.94495812786e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.794264778088\n",
      "\n",
      " \t the posterior prob is propotional to 0.264754926029\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.5780055487974161e-81, 3.944958127864993e-05, 0.26475492602940986])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.72889078e-80   1.48981946e-04   9.99851018e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 132th row with id : 133 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 5.6\n",
      "Petal Width : 2.2\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.35981985281e-199\n",
      "\n",
      " \t the posterior prob is propotional to 7.86606617604e-200\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.549683883078\n",
      "\n",
      " \t the posterior prob is propotional to 0.183227961026\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.09954360227e-06\n",
      "\n",
      " \t the posterior prob is propotional to 3.66514534091e-07\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.8660661760394227e-200, 0.18322796102589495, 3.6651453409077906e-07])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.29304043e-199   9.99998000e-001   2.00031588e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 73th row with id : 74 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.7\n",
      "Petal Width : 1.2\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.52446929219e-95\n",
      "\n",
      " \t the posterior prob is propotional to 1.1748230974e-95\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00173151237182\n",
      "\n",
      " \t the posterior prob is propotional to 0.000577170790608\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.838713529444\n",
      "\n",
      " \t the posterior prob is propotional to 0.279571176481\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1748230973954332e-95, 0.00057717079060779072, 0.27957117648143204])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.19357497e-95   2.06023272e-03   9.97939767e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 63th row with id : 64 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.7\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.45564130965e-103\n",
      "\n",
      " \t the posterior prob is propotional to 1.81854710322e-103\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0133713874484\n",
      "\n",
      " \t the posterior prob is propotional to 0.00445712914945\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.88324019762\n",
      "\n",
      " \t the posterior prob is propotional to 0.294413399207\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.8185471032174803e-103, 0.0044571291494527225, 0.29441339920665127])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.08473212e-103   1.49132441e-002   9.85086756e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 122th row with id : 123 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.7\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 6.7\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.66644191601e-269\n",
      "\n",
      " \t the posterior prob is propotional to 1.888813972e-269\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0174708091019\n",
      "\n",
      " \t the posterior prob is propotional to 0.00582360303398\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.04560882999e-11\n",
      "\n",
      " \t the posterior prob is propotional to 6.81869609998e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.8888139720044832e-269, 0.0058236030339831046, 6.8186960999769195e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.24337692e-267   9.99999999e-001   1.17087241e-009]]\n",
      "\n",
      "\n",
      "For the sample in the 5th row with id : 6 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.9\n",
      "Petal Length : 1.7\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.335506729733\n",
      "\n",
      " \t the posterior prob is propotional to 0.111835576578\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.49174505427e-21\n",
      "\n",
      " \t the posterior prob is propotional to 4.97248351423e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 9.33217420696e-15\n",
      "\n",
      " \t the posterior prob is propotional to 3.11072473565e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.11183557657759574, 4.9724835142261223e-22, 3.1107247356531975e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   4.44624481e-21   2.78151625e-14]]\n",
      "\n",
      "\n",
      "For the sample in the 96th row with id : 97 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.2\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.04652951426e-76\n",
      "\n",
      " \t the posterior prob is propotional to 1.68217650475e-76\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000452639421884\n",
      "\n",
      " \t the posterior prob is propotional to 0.000150879807295\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.36805189792\n",
      "\n",
      " \t the posterior prob is propotional to 0.456017299306\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.6821765047527671e-76, 0.00015087980729470093, 0.45601729930563573])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.68762352e-76   3.30754783e-04   9.99669245e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 25th row with id : 26 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.75489563105\n",
      "\n",
      " \t the posterior prob is propotional to 1.25163187702\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 6.64424093457e-23\n",
      "\n",
      " \t the posterior prob is propotional to 2.21474697819e-23\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.49525235098e-15\n",
      "\n",
      " \t the posterior prob is propotional to 8.31750783659e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.2516318770177111, 2.2147469781912529e-23, 8.3175078365879014e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.76948751e-23   6.64533078e-16]]\n",
      "\n",
      "\n",
      "For the sample in the 101th row with id : 102 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 5.1\n",
      "Petal Width : 1.9\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.28739885769e-149\n",
      "\n",
      " \t the posterior prob is propotional to 3.09579961923e-149\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.169640740284\n",
      "\n",
      " \t the posterior prob is propotional to 0.0565469134282\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00475114316053\n",
      "\n",
      " \t the posterior prob is propotional to 0.00158371438684\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.0957996192288027e-149, 0.056546913428150186, 0.001583714386843839])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.32559123e-148   9.72755939e-001   2.72440613e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 100th row with id : 101 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 6.0\n",
      "Petal Width : 2.5\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.17029670624e-247\n",
      "\n",
      " \t the posterior prob is propotional to 1.05676556875e-247\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0715831276122\n",
      "\n",
      " \t the posterior prob is propotional to 0.0238610425374\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 7.38044702975e-12\n",
      "\n",
      " \t the posterior prob is propotional to 2.46014900992e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.0567655687462284e-247, 0.023861042537402621, 2.4601490099164795e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.42883234e-246   1.00000000e+000   1.03103165e-010]]\n",
      "\n",
      "\n",
      "For the sample in the 7th row with id : 8 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.10981184269\n",
      "\n",
      " \t the posterior prob is propotional to 3.03660394756\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.48747659235e-24\n",
      "\n",
      " \t the posterior prob is propotional to 2.49582553078e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.2750365988e-16\n",
      "\n",
      " \t the posterior prob is propotional to 4.250121996e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.0366039475639441, 2.4958255307837209e-24, 4.2501219960019404e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   8.21913418e-25   1.39963000e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 43th row with id : 44 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.6\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0293834683647\n",
      "\n",
      " \t the posterior prob is propotional to 0.00979448945491\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.79022925811e-20\n",
      "\n",
      " \t the posterior prob is propotional to 3.2634097527e-20\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.83202372705e-12\n",
      "\n",
      " \t the posterior prob is propotional to 9.44007909018e-13\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.0097944894549094851, 3.2634097527048225e-20, 9.4400790901792317e-13])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.33188347e-18   9.63815330e-11]]\n",
      "\n",
      "\n",
      "For the sample in the 46th row with id : 47 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.00216401756\n",
      "\n",
      " \t the posterior prob is propotional to 1.33405467252\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.66897135832e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.22299045277e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.08289740223e-17\n",
      "\n",
      " \t the posterior prob is propotional to 6.94299134077e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.3340546725214888, 1.2229904527721286e-24, 6.9429913407747721e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   9.16746875e-25   5.20442789e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 22th row with id : 23 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.6\n",
      "Sepal Width : 3.6\n",
      "Petal Length : 1.0\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.119924804774\n",
      "\n",
      " \t the posterior prob is propotional to 0.0399749349246\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.97996623079e-28\n",
      "\n",
      " \t the posterior prob is propotional to 1.32665541026e-28\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.76664331611e-21\n",
      "\n",
      " \t the posterior prob is propotional to 1.9222144387e-21\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.039974934924576419, 1.3266554102622531e-28, 1.9222144387028039e-21])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.31871812e-27   4.80854926e-20]]\n",
      "\n",
      "\n",
      "For the sample in the 8th row with id : 9 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.4\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.788342226236\n",
      "\n",
      " \t the posterior prob is propotional to 0.262780742079\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.75554829019e-25\n",
      "\n",
      " \t the posterior prob is propotional to 9.1851609673e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.52059272605e-17\n",
      "\n",
      " \t the posterior prob is propotional to 5.06864242015e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.26278074207876156, 9.1851609673018169e-26, 5.0686424201503862e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.49537066e-25   1.92884851e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 115th row with id : 116 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 5.3\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.4943142585e-189\n",
      "\n",
      " \t the posterior prob is propotional to 1.1647714195e-189\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.334263630192\n",
      "\n",
      " \t the posterior prob is propotional to 0.111421210064\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.04849763761e-07\n",
      "\n",
      " \t the posterior prob is propotional to 6.8283254587e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1647714194996186e-189, 0.11142121006412878, 6.8283254587019109e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.04537610e-188   9.99999387e-001   6.12838549e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 41th row with id : 42 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.5\n",
      "Sepal Width : 2.3\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0272735728758\n",
      "\n",
      " \t the posterior prob is propotional to 0.0090911909586\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.43277979725e-25\n",
      "\n",
      " \t the posterior prob is propotional to 4.77593265748e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.95363224913e-17\n",
      "\n",
      " \t the posterior prob is propotional to 1.31787741638e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.0090911909585960106, 4.7759326574844341e-26, 1.3178774163753847e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   5.25336304e-24   1.44962021e-15]]\n",
      "\n",
      "\n",
      "For the sample in the 70th row with id : 71 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.9\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 4.8\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.36719034535e-127\n",
      "\n",
      " \t the posterior prob is propotional to 1.12239678178e-127\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.100015791765\n",
      "\n",
      " \t the posterior prob is propotional to 0.0333385972551\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0191834564698\n",
      "\n",
      " \t the posterior prob is propotional to 0.00639448548993\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1223967817838656e-127, 0.033338597255091092, 0.0063944854899295935])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.82484193e-126   8.39063948e-001   1.60936052e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 129th row with id : 130 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.2\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.8\n",
      "Petal Width : 1.6\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.72839805882e-179\n",
      "\n",
      " \t the posterior prob is propotional to 3.24279935294e-179\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.138767576392\n",
      "\n",
      " \t the posterior prob is propotional to 0.0462558587973\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.000114334787224\n",
      "\n",
      " \t the posterior prob is propotional to 3.81115957412e-05\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.2427993529409054e-179, 0.046255858797278601, 3.8111595741245209e-05])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.00479852e-178   9.99176748e-001   8.23251828e-004]]\n",
      "\n",
      "\n",
      "For the sample in the 10th row with id : 11 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.7\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.71371986663\n",
      "\n",
      " \t the posterior prob is propotional to 1.23790662221\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 5.61168328358e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.87056109453e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.57568435715e-17\n",
      "\n",
      " \t the posterior prob is propotional to 1.19189478572e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.2379066222088597, 1.8705610945276157e-24, 1.1918947857154842e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.51106801e-24   9.62830931e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 77th row with id : 78 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.0\n",
      "Petal Width : 1.7\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.13218011405e-135\n",
      "\n",
      " \t the posterior prob is propotional to 1.04406003802e-135\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.239767589278\n",
      "\n",
      " \t the posterior prob is propotional to 0.0799225297592\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0208199180319\n",
      "\n",
      " \t the posterior prob is propotional to 0.0069399726773\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.0440600380175595e-135, 0.079922529759188385, 0.0069399726773013886])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.20196864e-134   9.20103929e-001   7.98960712e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 51th row with id : 52 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.79235438139e-99\n",
      "\n",
      " \t the posterior prob is propotional to 5.97451460462e-100\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0158498511353\n",
      "\n",
      " \t the posterior prob is propotional to 0.00528328371176\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.261868448034\n",
      "\n",
      " \t the posterior prob is propotional to 0.0872894826779\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.9745146046192693e-100, 0.0052832837117610778, 0.087289482677921151])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.45385769e-99   5.70716844e-02   9.42928316e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 95th row with id : 96 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.2\n",
      "Petal Width : 1.2\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.40705014149e-72\n",
      "\n",
      " \t the posterior prob is propotional to 1.46901671383e-72\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000165577545228\n",
      "\n",
      " \t the posterior prob is propotional to 5.5192515076e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.938236581806\n",
      "\n",
      " \t the posterior prob is propotional to 0.312745527269\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.4690167138290992e-72, 5.5192515075993389e-05, 0.31274552726851479])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.69633419e-72   1.76446253e-04   9.99823554e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 134th row with id : 135 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 2.6\n",
      "Petal Length : 5.6\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.91585469951e-151\n",
      "\n",
      " \t the posterior prob is propotional to 6.38618233169e-152\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0229845829339\n",
      "\n",
      " \t the posterior prob is propotional to 0.00766152764464\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0220919961419\n",
      "\n",
      " \t the posterior prob is propotional to 0.00736399871398\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([6.3861823316946422e-152, 0.0076615276446385123, 0.0073639987139780868])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.25022204e-150   5.09900782e-001   4.90099218e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 53th row with id : 54 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 2.3\n",
      "Petal Length : 4.0\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.79947984023e-69\n",
      "\n",
      " \t the posterior prob is propotional to 5.99826613408e-70\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.23712373823e-05\n",
      "\n",
      " \t the posterior prob is propotional to 4.1237457941e-06\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.326408594673\n",
      "\n",
      " \t the posterior prob is propotional to 0.108802864891\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.9982661340833394e-70, 4.1237457941010806e-06, 0.10880286489107668])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.51275815e-69   3.78996409e-05   9.99962100e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 119th row with id : 120 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 2.2\n",
      "Petal Length : 5.0\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.18560263658e-123\n",
      "\n",
      " \t the posterior prob is propotional to 3.95200878859e-124\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00289026733099\n",
      "\n",
      " \t the posterior prob is propotional to 0.000963422443664\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0630412862361\n",
      "\n",
      " \t the posterior prob is propotional to 0.0210137620787\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.9520087885925066e-124, 0.00096342244366395824, 0.02101376207871206])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.79823252e-122   4.38373916e-002   9.56162608e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 114th row with id : 115 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 5.1\n",
      "Petal Width : 2.4\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.44130529155e-184\n",
      "\n",
      " \t the posterior prob is propotional to 4.80435097182e-185\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.09249308182\n",
      "\n",
      " \t the posterior prob is propotional to 0.0308310272733\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.28865854888e-07\n",
      "\n",
      " \t the posterior prob is propotional to 4.29552849628e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.804350971820652e-185, 0.03083102727334543, 4.2955284962795882e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.55828226e-183   9.99998607e-001   1.39324664e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 18th row with id : 19 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 1.7\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.305497910944\n",
      "\n",
      " \t the posterior prob is propotional to 0.101832636981\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 8.10997974287e-22\n",
      "\n",
      " \t the posterior prob is propotional to 2.70332658096e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.55769944926e-15\n",
      "\n",
      " \t the posterior prob is propotional to 1.18589981642e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.10183263698120432, 2.7033265809573632e-22, 1.1858998164216355e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.65467601e-21   1.16455770e-14]]\n",
      "\n",
      "\n",
      "For the sample in the 45th row with id : 46 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.8\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.81670564872\n",
      "\n",
      " \t the posterior prob is propotional to 1.27223521624\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.12248621662e-23\n",
      "\n",
      " \t the posterior prob is propotional to 7.07495405539e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.47458939131e-15\n",
      "\n",
      " \t the posterior prob is propotional to 4.91529797105e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.272235216241123, 7.0749540553862e-24, 4.9152979710464891e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   5.56104246e-24   3.86351353e-16]]\n",
      "\n",
      "\n",
      "For the sample in the 146th row with id : 147 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 5.0\n",
      "Petal Width : 1.9\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 6.7125561691e-146\n",
      "\n",
      " \t the posterior prob is propotional to 2.23751872303e-146\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.136311734642\n",
      "\n",
      " \t the posterior prob is propotional to 0.0454372448807\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00388423456095\n",
      "\n",
      " \t the posterior prob is propotional to 0.00129474485365\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.2375187230341716e-146, 0.045437244880693992, 0.0012947448536495682])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.78798086e-145   9.72294249e-001   2.77057506e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 59th row with id : 60 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.2\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 3.9\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.32276785597e-68\n",
      "\n",
      " \t the posterior prob is propotional to 4.40922618658e-69\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 4.42590116139e-05\n",
      "\n",
      " \t the posterior prob is propotional to 1.47530038713e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.412959221656\n",
      "\n",
      " \t the posterior prob is propotional to 0.137653073885\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.4092261865795741e-69, 1.4753003871300381e-05, 0.13765307388533402])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.20280075e-68   1.07163774e-04   9.99892836e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 35th row with id : 36 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 1.2\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.48634363665\n",
      "\n",
      " \t the posterior prob is propotional to 0.828781212218\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.23447584019e-25\n",
      "\n",
      " \t the posterior prob is propotional to 7.44825280065e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 7.17863847957e-18\n",
      "\n",
      " \t the posterior prob is propotional to 2.39287949319e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.828781212218067, 7.4482528006484405e-26, 2.3928794931916013e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   8.98699523e-26   2.88722700e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 69th row with id : 70 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 3.9\n",
      "Petal Width : 1.1\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.05271643933e-58\n",
      "\n",
      " \t the posterior prob is propotional to 1.01757214644e-58\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.18961453568e-06\n",
      "\n",
      " \t the posterior prob is propotional to 1.06320484523e-06\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.364942985188\n",
      "\n",
      " \t the posterior prob is propotional to 0.121647661729\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.0175721464443606e-58, 1.0632048452278863e-06, 0.12164766172931313])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.36484022e-58   8.73995881e-06   9.99991260e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 133th row with id : 134 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 5.1\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.23379991549e-128\n",
      "\n",
      " \t the posterior prob is propotional to 7.44599971831e-129\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.072649152833\n",
      "\n",
      " \t the posterior prob is propotional to 0.0242163842777\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.179512768464\n",
      "\n",
      " \t the posterior prob is propotional to 0.059837589488\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.4459997183082878e-129, 0.024216384277669735, 0.059837589488028586])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.85859334e-128   2.88105169e-001   7.11894831e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 107th row with id : 108 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.3\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 6.3\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 9.61987017746e-224\n",
      "\n",
      " \t the posterior prob is propotional to 3.20662339249e-224\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.120644805547\n",
      "\n",
      " \t the posterior prob is propotional to 0.0402149351822\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.14995046123e-07\n",
      "\n",
      " \t the posterior prob is propotional to 7.16650153743e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.206623392486729e-224, 0.040214935182235789, 7.1665015374326757e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.97369849e-223   9.99998218e-001   1.78204658e-006]]\n",
      "\n",
      "\n",
      "For the sample in the 44th row with id : 45 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 1.9\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0873776933208\n",
      "\n",
      " \t the posterior prob is propotional to 0.0291258977736\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.50768005616e-20\n",
      "\n",
      " \t the posterior prob is propotional to 5.02560018721e-21\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.19812001473e-13\n",
      "\n",
      " \t the posterior prob is propotional to 3.99373338244e-14\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.029125897773601837, 5.0256001872097884e-21, 3.9937333824407065e-14])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.72547477e-19   1.37119666e-12]]\n",
      "\n",
      "\n",
      "For the sample in the 149th row with id : 150 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.9\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.1\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.78185788207e-142\n",
      "\n",
      " \t the posterior prob is propotional to 5.93952627357e-143\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.230571000394\n",
      "\n",
      " \t the posterior prob is propotional to 0.0768570001312\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0146857355048\n",
      "\n",
      " \t the posterior prob is propotional to 0.00489524516828\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.939526273572048e-143, 0.076857000131182393, 0.0048952451682812642])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.26527602e-142   9.40120970e-001   5.98790302e-002]]\n",
      "\n",
      "\n",
      "For the sample in the 148th row with id : 149 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.2\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 5.4\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.18138009806e-194\n",
      "\n",
      " \t the posterior prob is propotional to 2.72712669935e-194\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.16548777142\n",
      "\n",
      " \t the posterior prob is propotional to 0.0551625904734\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.60036590152e-08\n",
      "\n",
      " \t the posterior prob is propotional to 1.86678863384e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.7271266993533308e-194, 0.055162590473416651, 1.8667886338391438e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.94379570e-193   9.99999662e-001   3.38415579e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 99th row with id : 100 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.1\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.55715206979e-72\n",
      "\n",
      " \t the posterior prob is propotional to 8.52384023263e-73\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000253553656921\n",
      "\n",
      " \t the posterior prob is propotional to 8.45178856403e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.41173030931\n",
      "\n",
      " \t the posterior prob is propotional to 0.470576769769\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.5238402326335585e-73, 8.4517885640268659e-05, 0.47057676976904583])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.81103491e-72   1.79572631e-04   9.99820427e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 26th row with id : 27 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.58380742376\n",
      "\n",
      " \t the posterior prob is propotional to 0.861269141253\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.70648604259e-21\n",
      "\n",
      " \t the posterior prob is propotional to 9.02162014198e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 8.26747568603e-14\n",
      "\n",
      " \t the posterior prob is propotional to 2.75582522868e-14\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.86126914125253173, 9.0216201419770877e-22, 2.7558252286756067e-14])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.04747978e-21   3.19972596e-14]]\n",
      "\n",
      "\n",
      "For the sample in the 111th row with id : 112 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 5.3\n",
      "Petal Width : 1.9\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.84951652502e-162\n",
      "\n",
      " \t the posterior prob is propotional to 2.61650550834e-162\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.440959447289\n",
      "\n",
      " \t the posterior prob is propotional to 0.14698648243\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00140168464644\n",
      "\n",
      " \t the posterior prob is propotional to 0.00046722821548\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.6165055083383683e-162, 0.14698648242977388, 0.00046722821547964008])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.77445891e-161   9.96831357e-001   3.16864332e-003]]\n",
      "\n",
      "\n",
      "For the sample in the 137th row with id : 138 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 5.5\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.68731917173e-166\n",
      "\n",
      " \t the posterior prob is propotional to 5.62439723908e-167\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.51288079754\n",
      "\n",
      " \t the posterior prob is propotional to 0.170960265847\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00112412305104\n",
      "\n",
      " \t the posterior prob is propotional to 0.000374707683679\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.6243972390848881e-167, 0.17096026584658491, 0.000374707683678748])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.28269070e-166   9.97813011e-001   2.18698889e-003]]\n",
      "\n",
      "\n",
      "For the sample in the 116th row with id : 117 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.5\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.5\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.09621893659e-167\n",
      "\n",
      " \t the posterior prob is propotional to 1.3654063122e-167\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.570918782106\n",
      "\n",
      " \t the posterior prob is propotional to 0.190306260702\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00123175041156\n",
      "\n",
      " \t the posterior prob is propotional to 0.000410583470521\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.365406312196649e-167, 0.19030626070193837, 0.0004105834705211926])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.15933780e-167   9.97847157e-001   2.15284325e-003]]\n",
      "\n",
      "\n",
      "For the sample in the 128th row with id : 129 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 5.6\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.75553634117e-192\n",
      "\n",
      " \t the posterior prob is propotional to 1.25184544706e-192\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.647894839881\n",
      "\n",
      " \t the posterior prob is propotional to 0.215964946627\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 9.04291998636e-06\n",
      "\n",
      " \t the posterior prob is propotional to 3.01430666212e-06\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.2518454470577895e-192, 0.21596494662701066, 3.0143066621203857e-06])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.79644055e-192   9.99986043e-001   1.39571937e-005]]\n",
      "\n",
      "\n",
      "For the sample in the 30th row with id : 31 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.8\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 1.6\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.07925551375\n",
      "\n",
      " \t the posterior prob is propotional to 1.35975183792\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.6797979714e-23\n",
      "\n",
      " \t the posterior prob is propotional to 8.93265990468e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 8.62737400603e-16\n",
      "\n",
      " \t the posterior prob is propotional to 2.87579133534e-16\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.3597518379151046, 8.9326599046769526e-24, 2.8757913353431896e-16])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   6.56933100e-24   2.11493837e-16]]\n",
      "\n",
      "\n",
      "For the sample in the 27th row with id : 28 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.2\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.65991817759\n",
      "\n",
      " \t the posterior prob is propotional to 2.5533060592\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.89041925231e-24\n",
      "\n",
      " \t the posterior prob is propotional to 3.29680641744e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.19716425899e-16\n",
      "\n",
      " \t the posterior prob is propotional to 3.99054752997e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.553306059195326, 3.2968064174352688e-24, 3.9905475299692405e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.29119124e-24   1.56289432e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 2th row with id : 3 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.7\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.4728272483\n",
      "\n",
      " \t the posterior prob is propotional to 1.15760908277\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.52668406285e-25\n",
      "\n",
      " \t the posterior prob is propotional to 8.4222802095e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 8.25988358296e-18\n",
      "\n",
      " \t the posterior prob is propotional to 2.75329452765e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.157609082765968, 8.4222802094994686e-26, 2.7532945276519007e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   7.27558235e-26   2.37843204e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 138th row with id : 139 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.8\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.01636829503e-127\n",
      "\n",
      " \t the posterior prob is propotional to 3.38789431678e-128\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.149218721539\n",
      "\n",
      " \t the posterior prob is propotional to 0.0497395738462\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0373022154966\n",
      "\n",
      " \t the posterior prob is propotional to 0.0124340718322\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.3878943167772337e-128, 0.049739573846194818, 0.012434071832184812])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.44908422e-127   8.00010572e-001   1.99989428e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 109th row with id : 110 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.2\n",
      "Sepal Width : 3.6\n",
      "Petal Length : 6.1\n",
      "Petal Width : 2.5\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.34723956725e-259\n",
      "\n",
      " \t the posterior prob is propotional to 7.82413189083e-260\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.010737600069\n",
      "\n",
      " \t the posterior prob is propotional to 0.003579200023\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 2.64323386397e-14\n",
      "\n",
      " \t the posterior prob is propotional to 8.81077954657e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.8241318908302333e-260, 0.0035792000230027818, 8.8107795465664979e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.18600018e-257   1.00000000e+000   2.46166168e-012]]\n",
      "\n",
      "\n",
      "For the sample in the 62th row with id : 63 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 2.2\n",
      "Petal Length : 4.0\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.50582885307e-61\n",
      "\n",
      " \t the posterior prob is propotional to 2.50194295102e-61\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 5.33441746076e-07\n",
      "\n",
      " \t the posterior prob is propotional to 1.77813915359e-07\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0707357534647\n",
      "\n",
      " \t the posterior prob is propotional to 0.0235785844882\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.5019429510217792e-61, 1.7781391535858686e-07, 0.023578584488218576])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.06110020e-59   7.54127435e-06   9.99992459e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 145th row with id : 146 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.2\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.56868146847e-185\n",
      "\n",
      " \t the posterior prob is propotional to 5.22893822823e-186\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.396736234847\n",
      "\n",
      " \t the posterior prob is propotional to 0.132245411616\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.14038513043e-07\n",
      "\n",
      " \t the posterior prob is propotional to 1.04679504348e-07\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.2289382282276377e-186, 0.13224541161567729, 1.0467950434771537e-07])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.95396258e-185   9.99999208e-001   7.91554279e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 9th row with id : 10 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.71637515617\n",
      "\n",
      " \t the posterior prob is propotional to 0.905458385392\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.20596040171e-25\n",
      "\n",
      " \t the posterior prob is propotional to 3.06865346724e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.87886314321e-17\n",
      "\n",
      " \t the posterior prob is propotional to 6.26287714402e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.90545838539161227, 3.0686534672378497e-25, 6.2628771440215517e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.38906074e-25   6.91680285e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 98th row with id : 99 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 3.0\n",
      "Petal Width : 1.1\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.41214852765e-32\n",
      "\n",
      " \t the posterior prob is propotional to 2.47071617588e-32\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.38508072409e-09\n",
      "\n",
      " \t the posterior prob is propotional to 4.61693574697e-10\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00447559703612\n",
      "\n",
      " \t the posterior prob is propotional to 0.00149186567871\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.4707161758832345e-32, 4.6169357469655834e-10, 0.0014918656787066703])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.65612457e-29   3.09473861e-07   9.99999691e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 105th row with id : 106 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.6\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 6.6\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.41052815836e-267\n",
      "\n",
      " \t the posterior prob is propotional to 1.47017605279e-267\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0363848586082\n",
      "\n",
      " \t the posterior prob is propotional to 0.0121282862027\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.38533716251e-11\n",
      "\n",
      " \t the posterior prob is propotional to 4.61779054171e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.4701760527864761e-267, 0.012128286202738672, 4.6177905417134187e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.21218780e-265   1.00000000e+000   3.80745512e-010]]\n",
      "\n",
      "\n",
      "For the sample in the 94th row with id : 95 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 4.2\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.61703839556e-76\n",
      "\n",
      " \t the posterior prob is propotional to 1.20567946519e-76\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000256855130727\n",
      "\n",
      " \t the posterior prob is propotional to 8.56183769091e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.30600936036\n",
      "\n",
      " \t the posterior prob is propotional to 0.435336453455\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.2056794651851206e-76, 8.5618376909062804e-05, 0.43533645345473221])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.76899024e-76   1.96633066e-04   9.99803367e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 28th row with id : 29 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.2\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.4748256771\n",
      "\n",
      " \t the posterior prob is propotional to 2.49160855903\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 4.06536108606e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.35512036202e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 6.68963860235e-17\n",
      "\n",
      " \t the posterior prob is propotional to 2.22987953412e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.4916085590345309, 1.3551203620191019e-24, 2.229879534115742e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   5.43873698e-25   8.94955801e-18]]\n",
      "\n",
      "\n",
      "For the sample in the 141th row with id : 142 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 5.1\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.33726391414e-181\n",
      "\n",
      " \t the posterior prob is propotional to 7.79087971381e-182\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.291009070584\n",
      "\n",
      " \t the posterior prob is propotional to 0.0970030235281\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.84868369357e-07\n",
      "\n",
      " \t the posterior prob is propotional to 6.16227897857e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.7908797138077602e-182, 0.097003023528085125, 6.1622789785703154e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.03157931e-181   9.99999365e-001   6.35266288e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 66th row with id : 67 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.6\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 6.96107784718e-97\n",
      "\n",
      " \t the posterior prob is propotional to 2.32035928239e-97\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00630970646238\n",
      "\n",
      " \t the posterior prob is propotional to 0.00210323548746\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.620341402737\n",
      "\n",
      " \t the posterior prob is propotional to 0.206780467579\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.3203592823921916e-97, 0.0021032354874607403, 0.20678046757910909])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.11083787e-96   1.00689305e-02   9.89931070e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 102th row with id : 103 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.1\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.9\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.17274651482e-214\n",
      "\n",
      " \t the posterior prob is propotional to 3.90915504942e-215\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.464312472863\n",
      "\n",
      " \t the posterior prob is propotional to 0.154770824288\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.08068184353e-07\n",
      "\n",
      " \t the posterior prob is propotional to 3.60227281177e-08\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.9091550494163324e-215, 0.1547708242876501, 3.6022728117675346e-08])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.52576941e-214   9.99999767e-001   2.32748775e-007]]\n",
      "\n",
      "\n",
      "For the sample in the 83th row with id : 84 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 5.1\n",
      "Petal Width : 1.6\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.5949037833e-132\n",
      "\n",
      " \t the posterior prob is propotional to 8.64967927766e-133\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0795447924902\n",
      "\n",
      " \t the posterior prob is propotional to 0.0265149308301\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.126228856398\n",
      "\n",
      " \t the posterior prob is propotional to 0.0420762854658\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.6496792776570547e-133, 0.026514930830082675, 0.042076285465849968])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.26104766e-131   3.86564523e-001   6.13435477e-001]]\n",
      "\n",
      "\n",
      "For the sample in the 103th row with id : 104 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.3\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 5.6\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.56984369942e-172\n",
      "\n",
      " \t the posterior prob is propotional to 1.18994789981e-172\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.508689178772\n",
      "\n",
      " \t the posterior prob is propotional to 0.169563059591\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0011680595954\n",
      "\n",
      " \t the posterior prob is propotional to 0.000389353198465\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1899478998072165e-172, 0.16956305959065071, 0.00038935319846516493])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  7.00165346e-172   9.97709046e-001   2.29095423e-003]]\n",
      "\n",
      "\n",
      "For the sample in the 14th row with id : 15 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 4.0\n",
      "Petal Length : 1.2\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0721560367933\n",
      "\n",
      " \t the posterior prob is propotional to 0.0240520122644\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.90004321689e-26\n",
      "\n",
      " \t the posterior prob is propotional to 6.33347738962e-27\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 4.23117541556e-20\n",
      "\n",
      " \t the posterior prob is propotional to 1.41039180519e-20\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.024052012264426714, 6.3334773896245509e-27, 1.4103918051856071e-20])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.63324221e-25   5.86392436e-19]]\n",
      "\n",
      "\n",
      "For the sample in the 147th row with id : 148 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.5\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.2\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.22685385478e-163\n",
      "\n",
      " \t the posterior prob is propotional to 2.74228461826e-163\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.653512952546\n",
      "\n",
      " \t the posterior prob is propotional to 0.217837650849\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.000287567778968\n",
      "\n",
      " \t the posterior prob is propotional to 9.58559263227e-05\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.7422846182598839e-163, 0.21783765084861689, 9.5855926322714887e-05])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.25831253e-162   9.99560160e-001   4.39840242e-004]]\n",
      "\n",
      "\n",
      "For the sample in the 108th row with id : 109 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 5.8\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.41791536835e-187\n",
      "\n",
      " \t the posterior prob is propotional to 8.05971789449e-188\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.175546977485\n",
      "\n",
      " \t the posterior prob is propotional to 0.0585156591615\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.000102283912996\n",
      "\n",
      " \t the posterior prob is propotional to 3.40946376654e-05\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.0597178944940654e-188, 0.058515659161518692, 3.4094637665374939e-05])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.37655880e-186   9.99417681e-001   5.82319061e-004]]\n",
      "\n",
      "\n",
      "For the sample in the 78th row with id : 79 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.91338311663e-98\n",
      "\n",
      " \t the posterior prob is propotional to 1.30446103888e-98\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0134442243826\n",
      "\n",
      " \t the posterior prob is propotional to 0.00448140812754\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.913466845441\n",
      "\n",
      " \t the posterior prob is propotional to 0.30448894848\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.3044610388775989e-98, 0.004481408127539506, 0.30448894848036046])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.22196179e-98   1.45043304e-02   9.85495670e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 13th row with id : 14 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.3\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.1\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.0335835440731\n",
      "\n",
      " \t the posterior prob is propotional to 0.011194514691\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.94793126447e-28\n",
      "\n",
      " \t the posterior prob is propotional to 6.4931042149e-29\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.78227373538e-21\n",
      "\n",
      " \t the posterior prob is propotional to 1.92742457846e-21\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.011194514691037612, 6.4931042149029696e-29, 1.9274245784613292e-21])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   5.80025521e-27   1.72175805e-19]]\n",
      "\n",
      "\n",
      "For the sample in the 74th row with id : 75 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.4\n",
      "Sepal Width : 2.9\n",
      "Petal Length : 4.3\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.34789110281e-82\n",
      "\n",
      " \t the posterior prob is propotional to 4.4929703427e-83\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0017615451599\n",
      "\n",
      " \t the posterior prob is propotional to 0.000587181719965\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.01857395772\n",
      "\n",
      " \t the posterior prob is propotional to 0.339524652574\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.492970342704906e-83, 0.0005871817199654811, 0.33952465257407094])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.32102735e-82   1.72643719e-03   9.98273563e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 39th row with id : 40 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.7928535191\n",
      "\n",
      " \t the posterior prob is propotional to 2.93095117303\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.09528763583e-23\n",
      "\n",
      " \t the posterior prob is propotional to 3.65095878611e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.7780490174e-16\n",
      "\n",
      " \t the posterior prob is propotional to 5.92683005802e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.9309511730336144, 3.6509587861077699e-24, 5.9268300580150383e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.24565664e-24   2.02215244e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 40th row with id : 41 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.52866290674\n",
      "\n",
      " \t the posterior prob is propotional to 1.84288763558\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.2663320313e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.08877734377e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 7.50890144822e-17\n",
      "\n",
      " \t the posterior prob is propotional to 2.50296714941e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.8428876355803214, 1.0887773437674434e-24, 2.5029671494065159e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   5.90799636e-25   1.35817676e-17]]\n",
      "\n",
      "\n",
      "For the sample in the 65th row with id : 66 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 4.4\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.62118896049e-92\n",
      "\n",
      " \t the posterior prob is propotional to 8.73729653496e-93\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00626627822656\n",
      "\n",
      " \t the posterior prob is propotional to 0.00208875940885\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.288738827187\n",
      "\n",
      " \t the posterior prob is propotional to 0.096246275729\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([8.7372965349602853e-93, 0.0020887594088541792, 0.096246275728980174])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.88523253e-92   2.12412535e-02   9.78758747e-01]]\n",
      "\n",
      "\n",
      "For the sample in the 135th row with id : 136 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.7\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 6.1\n",
      "Petal Width : 2.3\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.51449369596e-247\n",
      "\n",
      " \t the posterior prob is propotional to 5.04831231988e-248\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0653745446706\n",
      "\n",
      " \t the posterior prob is propotional to 0.0217915148902\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 9.46656110675e-12\n",
      "\n",
      " \t the posterior prob is propotional to 3.15552036892e-12\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.0483123198751388e-248, 0.021791514890192161, 3.1555203689162442e-12])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.31664129e-246   1.00000000e+000   1.44805003e-010]]\n",
      "\n",
      "\n",
      "For the sample in the 50th row with id : 51 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.0\n",
      "Sepal Width : 3.2\n",
      "Petal Length : 4.7\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.62163149483e-107\n",
      "\n",
      " \t the posterior prob is propotional to 5.4054383161e-108\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0116869949169\n",
      "\n",
      " \t the posterior prob is propotional to 0.00389566497229\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0472980983628\n",
      "\n",
      " \t the posterior prob is propotional to 0.0157660327876\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.4054383161022282e-108, 0.0038956649722921171, 0.015766032787598715])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.74922257e-106   1.98134720e-001   8.01865280e-001]]\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "[[ 35.   0.   0.]\n",
      " [  0.  44.   3.]\n",
      " [  0.   3.  35.]]\n",
      "\n",
      "\n",
      "The extent of rounding off errors are 0\n"
     ]
    }
   ],
   "source": [
    "predictedProb = {}\n",
    "\n",
    "# Posterior prob for Training set samples\n",
    "for index, row in train.iterrows():\n",
    "    print(\"\\n\\nFor the sample in the \"+str(index)+\"th row with id : \"+str(row[0])+\" the 4 features take the \\nfollowing values in cm,\\n\")\n",
    "    print(\"\\nSepal Length : \"+str(row[1])+\n",
    "          \"\\nSepal Width : \" +str(row[2])+\n",
    "          \"\\nPetal Length : \"+str(row[3])+\n",
    "          \"\\nPetal Width : \" +str(row[4]))\n",
    "    \n",
    "    assert (row[0] == index + 1) # Note id starts from 1 till 150 while index goes from 0 to 149\n",
    "    \n",
    "    actualClass = labelofClass(row[5])\n",
    "    print(\"\\nNote this sample is drawn from class no : \"+str(actualClass))\n",
    "    \n",
    "    # p(C_k | \\vec x) = predictedProb[indexOfX][k]\n",
    "    preNormalized = {}\n",
    "    \n",
    "    # Iterate over 3 classes and 4 features\n",
    "    for k in range(1,4):\n",
    "        likelyhood = 1\n",
    "        print(\"\\n\\n For class no \"+str(k))\n",
    "        for i in range(1,5):\n",
    "            likelyhood = likelyhood * pdfFeatureGivenClass(row[i],i,k)\n",
    "        print(\"\\n \\t the likelyhood is propotional to \"+str(likelyhood))\n",
    "        preNormalized[k] = classPriors[k]*likelyhood\n",
    "        print(\"\\n \\t the posterior prob is propotional to \"+str(preNormalized[k]))\n",
    "        \n",
    "    # To obtain actual posterior probabilities we normalize\n",
    "    predictedProb[index] = normalize(np.array(list(preNormalized.values())).reshape(1,-1), norm='l1')\n",
    "        \n",
    "    print(\"\\n Thus pre normalization the values were\")\n",
    "    print(preNormalized.values())\n",
    "    \n",
    "    print(\"\\n After normalization we get the probabilities\")\n",
    "    print(predictedProb[index])\n",
    "    \n",
    "\n",
    "confArrayTrain = np.zeros((3,3))\n",
    "# Classification using MAP rule\n",
    "for index, row in train.iterrows():\n",
    "    predictedClass = predictedProb[index].argmax() # 0 to 2 are the positions\n",
    "    actualClass = labelofClass(row[5]) # 1 to 3 are the class labels\n",
    "    confArrayTrain[actualClass-1][predictedClass] += 1\n",
    "    \n",
    "    print(\"Predicted : \"+str(predictedClass)+\" while true class : \"+str(actualClass-1)+\"\\n\\n\")\n",
    "    \n",
    "print(confArrayTrain)\n",
    "print(\"\\n\\nThe extent of rounding off errors are \"+str(error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Choosing a decision rule\n",
    "\n",
    "The rule I used above is the maximum a posteriori or MAP decision rule.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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+V4tsZQccAtwItCNcymxqs0bUwrbYbXOWXXEZnr7zOebOnkt9fT3HDeyFu/IBPnvvczpv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\nVAUlOxGpCkp2IlIVlOxEpCr8PxuWn5IeuXHWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabee6c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.set_size_inches(5, 4)\n",
    "\n",
    "# Plotting the confusion matrix after MAP classification on training set\n",
    "dfTraincm = pd.DataFrame(confArrayTrain, [1,2,3], [1,2,3])\n",
    "plt.title('Confusion Matrix on Training set')\n",
    "sn.heatmap(dfTraincm, annot=True)\n",
    "plt.show()\n",
    "# Horizontally - Actual Classes\n",
    "# Vertically - Predicted Classes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "For the sample in the 67th row with id : 68 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.8\n",
      "Sepal Width : 2.7\n",
      "Petal Length : 4.1\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.6511928304e-62\n",
      "\n",
      " \t the posterior prob is propotional to 5.50397610135e-63\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.71793448767e-06\n",
      "\n",
      " \t the posterior prob is propotional to 2.57264482922e-06\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.384482997041\n",
      "\n",
      " \t the posterior prob is propotional to 0.128160999014\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.5039761013482953e-63, 2.5726448292229023e-06, 0.12816099901369241])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.29449338e-62   2.00731362e-05   9.99979927e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 34th row with id : 35 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.71637515617\n",
      "\n",
      " \t the posterior prob is propotional to 0.905458385392\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 9.20596040171e-25\n",
      "\n",
      " \t the posterior prob is propotional to 3.06865346724e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.87886314321e-17\n",
      "\n",
      " \t the posterior prob is propotional to 6.26287714402e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.90545838539161227, 3.0686534672378497e-25, 6.2628771440215517e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.38906074e-25   6.91680285e-18]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 76th row with id : 77 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.8\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.8\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.96617464648e-111\n",
      "\n",
      " \t the posterior prob is propotional to 6.55391548827e-112\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0196112609909\n",
      "\n",
      " \t the posterior prob is propotional to 0.00653708699697\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.198840253085\n",
      "\n",
      " \t the posterior prob is propotional to 0.0662800843617\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([6.553915488267938e-112, 0.0065370869969660472, 0.066280084361704766])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  9.00050821e-111   8.97739760e-002   9.10226024e-001]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 33th row with id : 34 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 4.2\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.396916805241\n",
      "\n",
      " \t the posterior prob is propotional to 0.132305601747\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.77287650601e-26\n",
      "\n",
      " \t the posterior prob is propotional to 5.90958835337e-27\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.00435007433e-20\n",
      "\n",
      " \t the posterior prob is propotional to 1.00145002478e-20\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.13230560174708911, 5.9095883533745018e-27, 1.0014500247772362e-20])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   4.46661991e-26   7.56921862e-20]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 84th row with id : 85 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.54176334261e-96\n",
      "\n",
      " \t the posterior prob is propotional to 5.13921114202e-97\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00368375276295\n",
      "\n",
      " \t the posterior prob is propotional to 0.00122791758765\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.447189644308\n",
      "\n",
      " \t the posterior prob is propotional to 0.149063214769\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([5.139211142017975e-97, 0.0012279175876490482, 0.14906321476932177])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.41950391e-96   8.17025974e-03   9.91829740e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 19th row with id : 20 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.05455439316\n",
      "\n",
      " \t the posterior prob is propotional to 1.68485146439\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.03856218574e-23\n",
      "\n",
      " \t the posterior prob is propotional to 3.46187395247e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 9.56377859585e-17\n",
      "\n",
      " \t the posterior prob is propotional to 3.18792619862e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.6848514643874761, 3.4618739524685739e-24, 3.1879261986176704e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.05470573e-24   1.89211112e-17]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 131th row with id : 132 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 7.9\n",
      "Sepal Width : 3.8\n",
      "Petal Length : 6.4\n",
      "Petal Width : 2.0\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.45697281965e-248\n",
      "\n",
      " \t the posterior prob is propotional to 4.8565760655e-249\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00111573767489\n",
      "\n",
      " \t the posterior prob is propotional to 0.000371912558296\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 5.20925748561e-13\n",
      "\n",
      " \t the posterior prob is propotional to 1.73641916187e-13\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([4.856576065499584e-249, 0.00037191255829643779, 1.7364191618706274e-13])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.30583815e-245   1.00000000e+000   4.66889091e-010]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 6th row with id : 7 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.6\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.3\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.25231551873\n",
      "\n",
      " \t the posterior prob is propotional to 1.41743850624\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.49773509574e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.16591169858e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.01655017118e-16\n",
      "\n",
      " \t the posterior prob is propotional to 3.38850057061e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.4174385062443031, 1.1659116985795807e-24, 3.3885005706095511e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   8.22548346e-25   2.39058030e-17]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 91th row with id : 92 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.6\n",
      "Petal Width : 1.4\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.97025897159e-98\n",
      "\n",
      " \t the posterior prob is propotional to 9.90086323862e-99\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0101762360667\n",
      "\n",
      " \t the posterior prob is propotional to 0.0033920786889\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.877798120292\n",
      "\n",
      " \t the posterior prob is propotional to 0.292599373431\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([9.900863238623718e-99, 0.0033920786888986827, 0.29259937343067333])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.34498283e-98   1.14600562e-02   9.88539944e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 3th row with id : 4 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.6\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.31683596095\n",
      "\n",
      " \t the posterior prob is propotional to 1.10561198698\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.83079759732e-24\n",
      "\n",
      " \t the posterior prob is propotional to 9.43599199107e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 9.99861652066e-17\n",
      "\n",
      " \t the posterior prob is propotional to 3.33287217355e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1056119869825634, 9.4359919910743962e-25, 3.3328721735517935e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   8.53463250e-25   3.01450438e-17]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 89th row with id : 90 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 2.5\n",
      "Petal Length : 4.0\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.31479209712e-69\n",
      "\n",
      " \t the posterior prob is propotional to 2.43826403237e-69\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.73068533535e-05\n",
      "\n",
      " \t the posterior prob is propotional to 1.24356177845e-05\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.692046081481\n",
      "\n",
      " \t the posterior prob is propotional to 0.23068202716\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.4382640323726278e-69, 1.2435617784499352e-05, 0.23068202716038458])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.05692352e-68   5.39051420e-05   9.99946095e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 55th row with id : 56 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.10540553811e-88\n",
      "\n",
      " \t the posterior prob is propotional to 3.68468512703e-89\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.00131259976354\n",
      "\n",
      " \t the posterior prob is propotional to 0.000437533254513\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.31305661264\n",
      "\n",
      " \t the posterior prob is propotional to 0.437685537545\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.6846851270251633e-89, 0.00043753325451344481, 0.43768553754549339])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  8.41016000e-89   9.98653766e-04   9.99001346e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 36th row with id : 37 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.5\n",
      "Sepal Width : 3.5\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.18201397017\n",
      "\n",
      " \t the posterior prob is propotional to 0.727337990056\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.62220455841e-24\n",
      "\n",
      " \t the posterior prob is propotional to 5.40734852805e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.73669103609e-17\n",
      "\n",
      " \t the posterior prob is propotional to 5.78897012031e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.72733799005610122, 5.4073485280482853e-25, 5.7889701203093413e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   7.43443709e-25   7.95911969e-18]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 21th row with id : 22 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.1\n",
      "Sepal Width : 3.7\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.52626483678\n",
      "\n",
      " \t the posterior prob is propotional to 0.842088278928\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.0202599279e-22\n",
      "\n",
      " \t the posterior prob is propotional to 6.73419975968e-23\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.1387315648e-15\n",
      "\n",
      " \t the posterior prob is propotional to 1.04624385493e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.84208827892770755, 6.7341997596778142e-23, 1.0462438549327002e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   7.99702350e-23   1.24243964e-15]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 38th row with id : 39 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.4\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.745183971938\n",
      "\n",
      " \t the posterior prob is propotional to 0.248394657313\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.09725418085e-26\n",
      "\n",
      " \t the posterior prob is propotional to 2.36575139362e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 3.39074627561e-18\n",
      "\n",
      " \t the posterior prob is propotional to 1.13024875854e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.24839465731259527, 2.3657513936154929e-26, 1.1302487585364898e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   9.52416376e-26   4.55021364e-18]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 112th row with id : 113 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.8\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 5.5\n",
      "Petal Width : 2.1\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.5496471883e-188\n",
      "\n",
      " \t the posterior prob is propotional to 1.18321572943e-188\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.737674571752\n",
      "\n",
      " \t the posterior prob is propotional to 0.245891523917\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 4.59634675268e-06\n",
      "\n",
      " \t the posterior prob is propotional to 1.53211558423e-06\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.1832157294335827e-188, 0.24589152391726754, 1.532115584225918e-06])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  4.81191193e-188   9.99993769e-001   6.23082087e-006]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 68th row with id : 69 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.2\n",
      "Sepal Width : 2.2\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.02370760136e-100\n",
      "\n",
      " \t the posterior prob is propotional to 3.41235867121e-101\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000986289610763\n",
      "\n",
      " \t the posterior prob is propotional to 0.000328763203588\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.169051131726\n",
      "\n",
      " \t the posterior prob is propotional to 0.0563503772421\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.4123586712096611e-101, 0.00032876320358772495, 0.056350377242078198])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  6.02048416e-100   5.80042677e-003   9.94199573e-001]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 49th row with id : 50 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.0\n",
      "Sepal Width : 3.3\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 8.29797366918\n",
      "\n",
      " \t the posterior prob is propotional to 2.76599122306\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.79551904849e-24\n",
      "\n",
      " \t the posterior prob is propotional to 9.31839682828e-25\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 6.43675601215e-17\n",
      "\n",
      " \t the posterior prob is propotional to 2.14558533738e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.765991223060225, 9.3183968282846769e-25, 2.1455853373826928e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   3.36891771e-25   7.75702150e-18]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 57th row with id : 58 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 2.4\n",
      "Petal Length : 3.3\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.11467655924e-36\n",
      "\n",
      " \t the posterior prob is propotional to 7.04892186413e-37\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.11450603867e-09\n",
      "\n",
      " \t the posterior prob is propotional to 3.71502012889e-10\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.00357268676829\n",
      "\n",
      " \t the posterior prob is propotional to 0.00119089558943\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([7.0489218641256598e-37, 3.7150201288865296e-10, 0.0011908955894291066])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.91900728e-34   3.11951694e-07   9.99999688e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 86th row with id : 87 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.7\n",
      "Sepal Width : 3.1\n",
      "Petal Length : 4.7\n",
      "Petal Width : 1.5\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 3.21040437674e-110\n",
      "\n",
      " \t the posterior prob is propotional to 1.07013479225e-110\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.0360780748133\n",
      "\n",
      " \t the posterior prob is propotional to 0.0120260249378\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.141803750348\n",
      "\n",
      " \t the posterior prob is propotional to 0.0472679167828\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.0701347922462937e-110, 0.012026024937764494, 0.047267916782750885])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.80479618e-109   2.02820467e-001   7.97179533e-001]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 31th row with id : 32 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.84110848197\n",
      "\n",
      " \t the posterior prob is propotional to 0.613702827323\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 2.87150481651e-21\n",
      "\n",
      " \t the posterior prob is propotional to 9.57168272169e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 7.31578664197e-14\n",
      "\n",
      " \t the posterior prob is propotional to 2.43859554732e-14\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.61370282732293435, 9.5716827216856479e-22, 2.4385955473226929e-14])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.55966085e-21   3.97357718e-14]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 12th row with id : 13 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.8\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.77493296305\n",
      "\n",
      " \t the posterior prob is propotional to 0.591644321017\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.6759055488e-25\n",
      "\n",
      " \t the posterior prob is propotional to 5.58635182932e-26\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 4.65269108021e-18\n",
      "\n",
      " \t the posterior prob is propotional to 1.55089702674e-18\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.59164432101719311, 5.5863518293209694e-26, 1.5508970267350293e-18])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   9.44207800e-26   2.62133341e-18]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 85th row with id : 86 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.0\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 4.5\n",
      "Petal Width : 1.6\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.14472718126e-102\n",
      "\n",
      " \t the posterior prob is propotional to 3.81575727085e-103\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.010842302927\n",
      "\n",
      " \t the posterior prob is propotional to 0.00361410097568\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0748071200601\n",
      "\n",
      " \t the posterior prob is propotional to 0.0249357066867\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([3.8157572708500247e-103, 0.003614100975678573, 0.024935706686700521])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.33652644e-101   1.26589328e-001   8.73410672e-001]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 1th row with id : 2 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 4.9\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 1.4\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 4.5591842296\n",
      "\n",
      " \t the posterior prob is propotional to 1.51972807653\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.09747860212e-24\n",
      "\n",
      " \t the posterior prob is propotional to 1.03249286737e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.41493705097e-16\n",
      "\n",
      " \t the posterior prob is propotional to 4.71645683657e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.5197280765328651, 1.0324928673739046e-24, 4.7164568365712107e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   6.79393165e-25   3.10348733e-17]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 127th row with id : 128 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 3.0\n",
      "Petal Length : 4.9\n",
      "Petal Width : 1.8\n",
      "\n",
      "Note this sample is drawn from class no : 2\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 5.72370434497e-133\n",
      "\n",
      " \t the posterior prob is propotional to 1.90790144832e-133\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.214636094027\n",
      "\n",
      " \t the posterior prob is propotional to 0.0715453646758\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0273598000647\n",
      "\n",
      " \t the posterior prob is propotional to 0.00911993335489\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([1.9079014483246566e-133, 0.071545364675783721, 0.0091199333548884973])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  2.36520721e-132   8.86941057e-001   1.13058943e-001]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 71th row with id : 72 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 6.1\n",
      "Sepal Width : 2.8\n",
      "Petal Length : 4.0\n",
      "Petal Width : 1.3\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 7.73106711095e-70\n",
      "\n",
      " \t the posterior prob is propotional to 2.57702237032e-70\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 0.000305839496594\n",
      "\n",
      " \t the posterior prob is propotional to 0.000101946498865\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.35494638806\n",
      "\n",
      " \t the posterior prob is propotional to 0.451648796022\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([2.5770223703158491e-70, 0.00010194649886478869, 0.45164879602156205])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  5.70452271e-70   2.25669798e-04   9.99774330e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 32th row with id : 33 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.2\n",
      "Sepal Width : 4.1\n",
      "Petal Length : 1.5\n",
      "Petal Width : 0.1\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.697285950266\n",
      "\n",
      " \t the posterior prob is propotional to 0.232428650089\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.0085973067e-27\n",
      "\n",
      " \t the posterior prob is propotional to 2.33619910223e-27\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 1.11296996361e-20\n",
      "\n",
      " \t the posterior prob is propotional to 3.70989987871e-21\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.23242865008865077, 2.3361991022345074e-27, 3.7098998787056172e-21])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.00512527e-26   1.59614569e-20]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 20th row with id : 21 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.4\n",
      "Petal Length : 1.7\n",
      "Petal Width : 0.2\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 1.97650261822\n",
      "\n",
      " \t the posterior prob is propotional to 0.658834206073\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 3.95957478119e-22\n",
      "\n",
      " \t the posterior prob is propotional to 1.3198582604e-22\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 4.28277687414e-15\n",
      "\n",
      " \t the posterior prob is propotional to 1.42759229138e-15\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.65883420607326626, 1.3198582603960453e-22, 1.4275922913812439e-15])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   2.00332382e-22   2.16684604e-15]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 16th row with id : 17 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.4\n",
      "Sepal Width : 3.9\n",
      "Petal Length : 1.3\n",
      "Petal Width : 0.4\n",
      "\n",
      "Note this sample is drawn from class no : 1\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 0.541287218572\n",
      "\n",
      " \t the posterior prob is propotional to 0.180429072857\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 7.28932648922e-24\n",
      "\n",
      " \t the posterior prob is propotional to 2.42977549641e-24\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 6.29029452184e-17\n",
      "\n",
      " \t the posterior prob is propotional to 2.09676484061e-17\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([0.18042907285717424, 2.4297754964077816e-24, 2.0967648406138486e-17])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  1.00000000e+00   1.34666518e-23   1.16209922e-16]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "\n",
      "\n",
      "For the sample in the 79th row with id : 80 the 4 features take the \n",
      "following values in cm,\n",
      "\n",
      "\n",
      "Sepal Length : 5.7\n",
      "Sepal Width : 2.6\n",
      "Petal Length : 3.5\n",
      "Petal Width : 1.0\n",
      "\n",
      "Note this sample is drawn from class no : 3\n",
      "\n",
      "\n",
      " For class no 1\n",
      "\n",
      " \t the likelyhood is propotional to 2.92972432124e-42\n",
      "\n",
      " \t the posterior prob is propotional to 9.76574773748e-43\n",
      "\n",
      "\n",
      " For class no 2\n",
      "\n",
      " \t the likelyhood is propotional to 1.45664179654e-07\n",
      "\n",
      " \t the posterior prob is propotional to 4.85547265513e-08\n",
      "\n",
      "\n",
      " For class no 3\n",
      "\n",
      " \t the likelyhood is propotional to 0.0909505034612\n",
      "\n",
      " \t the posterior prob is propotional to 0.0303168344871\n",
      "\n",
      " Thus pre normalization the values were\n",
      "dict_values([9.7657477374776535e-43, 4.855472655133438e-08, 0.030316834487069316])\n",
      "\n",
      " After normalization we get the probabilities\n",
      "[[  3.22122420e-41   1.60157383e-06   9.99998398e-01]]\n",
      "\n",
      " --------------------------------------- \n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 1 while true class : 1\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 0 while true class : 0\n",
      "\n",
      "\n",
      "Predicted : 2 while true class : 2\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "The extent of rounding off errors are 0\n",
      "[[ 15.   0.   0.]\n",
      " [  0.   3.   0.]\n",
      " [  0.   0.  12.]]\n"
     ]
    }
   ],
   "source": [
    "# Classifying the testing set\n",
    "posteriorProb = {}\n",
    "errorRounding = 0\n",
    "\n",
    "# Calculating posterior probability\n",
    "for index, row in test.iterrows():\n",
    "    print(\"\\n\\nFor the sample in the \"+str(index)+\"th row with id : \"+str(row[0])+\" the 4 features take the \\nfollowing values in cm,\\n\")\n",
    "    print(\"\\nSepal Length : \"+str(row[1])+\n",
    "          \"\\nSepal Width : \" +str(row[2])+\n",
    "          \"\\nPetal Length : \"+str(row[3])+\n",
    "          \"\\nPetal Width : \" +str(row[4]))\n",
    "    \n",
    "    assert (row[0] == index + 1) # Note id starts from 1 till 150 while index goes from 0 to 149\n",
    "    \n",
    "    actualClass = labelofClass(row[5])\n",
    "    print(\"\\nNote this sample is drawn from class no : \"+str(actualClass))\n",
    "    \n",
    "    # p(C_k | \\vec x) = predictedProb[indexOfX][k]\n",
    "    preNormalized = {}\n",
    "    \n",
    "    # Iterate over 3 classes and 4 features\n",
    "    for k in range(1,4):\n",
    "        likelyhood = 1\n",
    "        print(\"\\n\\n For class no \"+str(k))\n",
    "        for i in range(1,5):\n",
    "            likelyhood = likelyhood * pdfFeatureGivenClass(row[i],i,k)\n",
    "        print(\"\\n \\t the likelyhood is propotional to \"+str(likelyhood))\n",
    "        preNormalized[k] = classPriors[k]*likelyhood\n",
    "        print(\"\\n \\t the posterior prob is propotional to \"+str(preNormalized[k]))\n",
    "\n",
    "    posteriorProb[index] = normalize(np.array(list(preNormalized.values())).reshape(1,-1), norm='l1')\n",
    "        \n",
    "    print(\"\\n Thus pre normalization the values were\")\n",
    "    print(preNormalized.values())\n",
    "    \n",
    "    print(\"\\n After normalization we get the probabilities\")\n",
    "    print(posteriorProb[index])\n",
    "    \n",
    "    errorRounding += abs(1 - posteriorProb[index].sum())\n",
    "    \n",
    "    print(\"\\n --------------------------------------- \\n\")\n",
    "\n",
    "confArrayTest = np.zeros((3,3))\n",
    "\n",
    "\n",
    "# Classification using MAP rule\n",
    "for index, row in test.iterrows():\n",
    "    predictedClass = posteriorProb[index].argmax() # 0 to 2 are the positions\n",
    "    actualClass = labelofClass(row[5]) # 1 to 3 are the class labels\n",
    "    confArrayTest[actualClass-1][predictedClass] += 1\n",
    "    \n",
    "    print(\"Predicted : \"+str(predictedClass)+\" while true class : \"+str(actualClass-1)+\"\\n\\n\")\n",
    "    \n",
    "print(\"\\n\\nThe extent of rounding off errors are \"+str(error))\n",
    "\n",
    "print(confArrayTest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4+z+BW4A9zGyDPMdsj5KliORSaChkfmRUTJZ/AzCzPmaWZefNgb7AEyXKpgIF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\nPxl0fvXwtkUFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabee71d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.set_size_inches(5,4)\n",
    "\n",
    "# Testing Set confusion\n",
    "dfTestcm = pd.DataFrame(confArrayTest, [1,2,3], [1,2,3])\n",
    "plt.title('Confusion Matrix on Testing set')\n",
    "sn.heatmap(dfTestcm, annot=True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other than the confusion matrix we can use [Micro and Macro averaged F1 measure](http://stats.stackexchange.com/a/44522/103024). \n",
    "\n",
    "For now lets try computing empirical error rate or misclassification rate,\n",
    "\n",
    "Let $g$ be a classifier, and $x_i$ and $y_i$ be respectively an instance in your test dataset and its actual class. If $n$ such examples exist in the testing set then,\n",
    "\n",
    "$$err(g)= \\frac{1}{n} \\sum_{i≤n}1_{g(x_i)≠y_i}$$\n",
    "\n",
    "So this is the fraction of incorrectly classfied classes.\n",
    "\n",
    "But this measure gives equal importance to all classes, but we should give more importance to underrepresented classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 15.   0.   0.]\n",
      " [  0.   3.   0.]\n",
      " [  0.   0.  12.]]\n",
      "\n",
      " \n",
      " The Misclassification rate is 0.0 \n",
      "\n",
      "Iris-virginica     47\n",
      "Iris-versicolor    38\n",
      "Iris-setosa        35\n",
      "Name: Species, dtype: int64\n",
      "Iris-setosa        15\n",
      "Iris-versicolor    12\n",
      "Iris-virginica      3\n",
      "Name: Species, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "print(confArrayTest)\n",
    "totalTest = test.count()[0]\n",
    "emperror = 0\n",
    "\n",
    "for i in range(3):\n",
    "    for j in range(3):\n",
    "        if(i == j):\n",
    "            continue\n",
    "        emperror = emperror + confArrayTest[i][j]\n",
    "        \n",
    "# Unweighted empirical error\n",
    "print(\"\\n \\n The Misclassification rate is \"+str(emperror/totalTest)+\" \\n\")\n",
    "\n",
    "\n",
    "print(train['Species'].value_counts())\n",
    "print(test['Species'].value_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Motivation for the independence assumption\n",
    "\n",
    "Now note how we used the Naive independence assumption - the assumption that each feature is conditionally independent of each other given the class in order to avoid modelling likelyhood as a multivariate distribution, rather we could now model it as $n$ univariate distributions. \n",
    "\n",
    "We could argue that the [Curse of dimensionality](https://en.wikipedia.org/wiki/Curse_of_dimensionality) is why we do this. [This](http://www.visiondummy.com/2014/04/curse-dimensionality-affect-classification/) is a great article for further reading.\n",
    "\n",
    "Consider we form a histogram with only sepal length as a feature, we can discretize the values to say 0.1 cm widths. Then we would have maybe around 20 bins.\n",
    "\n",
    "Once we add a new feature sepal width into the fray now we have $20\\times20$ number of bins! See how sparse the available data becomes? We don't observe many important combinations. So with a fixed number of training samples, the predictive power reduces as the dimensionality increases.\n",
    "\n",
    "So if we have $m$ bins and $n$ features, instead of $m^n$ bins we only have $m\\times n$ bins if we go for $n$ univariate distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iW31WoqDAjyNjTAfgj8BUa+0Hddy8G94zf0/Da/u/HlgHTALUThmbinC5ALgL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccb20b54e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccb20fa208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NA4EAnZ2drkbuRqNRNmzYQEtLy0Sd0WiU1atX09XVVXJ9TU1NE/Vlu3BGo1FW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccb0136d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccabee7630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  4.   5.  10.  10.   4.   1.   4.   4.  11.   5.   1.   4.   5.  10.   0.\n",
      "   0.   1.   4.   0.   2.   1.   2.   4.   5.   4.   5.   4.   1.   1.  10.\n",
      "   5.   1.   1.   1.   5.   5.   1.   5.  10.   4.   4.   0.  10.   4.   2.\n",
      "   5.   2.  10.   1.   5.]\n"
     ]
    }
   ],
   "source": [
    "# take only one feature\n",
    "oneFeatureSetosa = dfClasses[\"Iris-setosa\"][['SepalLengthCm','Species']]\n",
    "oneFeatureSetosa.plot.hist(bins=20)\n",
    "plt.legend(loc=2)\n",
    "plt.show()\n",
    "\n",
    "plt.boxplot(oneFeatureSetosa['SepalLengthCm'].values)\n",
    "plt.show()\n",
    "\n",
    "twoFeatureSetosa = dfClasses[\"Iris-setosa\"][['SepalLengthCm', 'SepalWidthCm', 'Species']]\n",
    "x = twoFeatureSetosa['SepalLengthCm'].values\n",
    "y = twoFeatureSetosa['SepalWidthCm'].values\n",
    "\n",
    "lenEdges, widthEdges = np.linspace(2.5, 6.5, 10), np.linspace(2, 5, 10)\n",
    "hist, lenEdges, widthEdges = np.histogram2d(x, y, (lenEdges, widthEdges))\n",
    "xidx = np.clip(np.digitize(x, lenEdges), 0, hist.shape[0]-1)\n",
    "yidx = np.clip(np.digitize(y, widthEdges), 0, hist.shape[1]-1)\n",
    "c = hist[xidx, yidx]\n",
    "plt.scatter(x, y, c=c)\n",
    "plt.show()\n",
    "plt.scatter(x, y, c='g')\n",
    "plt.show()\n",
    "\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But let us try using a bayesian classifier **without** the naive independence assumptions.\n",
    "\n",
    "So in the orginal bayes equation,\n",
    "\n",
    "$$ p(C_{k} \\ | \\ \\mathbf {x}) = \\frac {p(C_{k})\\ p(\\mathbf {x} \\mid C_{k})}{p(\\mathbf {x})} = \\frac {p(\\mathbf {x} , C_{k})}{p(\\mathbf {x})}$$\n",
    "\n",
    "Here we can model $p(\\mathbf {x} \\mid C_{k})$\n",
    "   as a multivariate guassian distribution, so we have two parameters we need to compute the mean vector $\\boldsymbol\\mu_k$ and the covariance matrix ($ \\boldsymbol\\Sigma_k$) for each class. Note there are $n$ features.\n",
    "\n",
    "$$p(\\mathbf {x} \\mid C_{k}) \\sim\\ \\mathcal{N}(\\boldsymbol\\mu_k,\\, \\boldsymbol\\Sigma_k)$$\n",
    "\n",
    "The P.D.F of this distribution is,\n",
    "\n",
    "$$\\Large f(\\mathbf {x} \\; \\ | \\; \\boldsymbol\\mu_k , \\boldsymbol\\Sigma_k) = \\frac{e^{\\frac{ {(\\mathbf {x}-\\boldsymbol\\mu_k)}^T {\\boldsymbol\\Sigma_k}^{\\mathbf{-1}}(\\mathbf {x} - \\boldsymbol\\mu_k)  }{2}}}{\\sqrt{{2\\pi}^n |\\boldsymbol\\Sigma_k|}}$$\n",
    "\n",
    "![Multivariate](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/MultivariateNormal.png/300px-MultivariateNormal.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Id                                                            9666\n",
      "SepalLengthCm                                                  709\n",
      "SepalWidthCm                                                 363.1\n",
      "PetalLengthCm                                                474.4\n",
      "PetalWidthCm                                                 154.6\n",
      "Species          Iris-virginicaIris-setosaIris-setosaIris-versi...\n",
      "dtype: object\n",
      "\n",
      " total no of instances in train = 120\n",
      "\n",
      "\n",
      "[ 5.90833333  3.02583333  3.95333333  1.28833333]\n",
      "\n",
      "\n",
      "[[ 4.48490686  4.48490686  4.48490686  4.48490686]\n",
      " [ 4.48490686  4.48490686  4.48490686  4.48490686]\n",
      " [ 4.48490686  4.48490686  4.48490686  4.48490686]\n",
      " [ 4.48490686  4.48490686  4.48490686  4.48490686]]\n"
     ]
    }
   ],
   "source": [
    "print(sum(train))\n",
    "print(\"\\n total no of instances in train = \"+str(totalCount)+\"\\n\\n\")\n",
    "x1 = sum(train)[1]/totalCount\n",
    "x2 = sum(train)[2]/totalCount\n",
    "x3 = sum(train)[3]/totalCount\n",
    "x4 = sum(train)[4]/totalCount\n",
    "\n",
    "# Sample mean \n",
    "xMean = np.array([x1,x2,x3,x4])\n",
    "\n",
    "print(xMean)\n",
    "print(\"\\n\")\n",
    "\n",
    "# lets compute sample covariance matrix (unbiased)\n",
    "q = np.zeros([4,4])\n",
    "\n",
    "for i in range(totalCount):\n",
    "    temp = np.array([train.iloc[i][1], train.iloc[i][2], train.iloc[i][3], train.iloc[i][4]])\n",
    "    q = q + np.matmul((temp - xMean),np.transpose(temp - xMean))\n",
    "    \n",
    "q = q/(totalCount-1)\n",
    "\n",
    "print(q)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# return f(\\vec x) for MULTIVARIATE GUASSIAN note no given class\n",
    "def pdfFeatureMultiVariate(x,k):\n",
    "    return(None)\n"
   ]
  }
 ],
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