notebooks/06-naive-bayes-uci-winery-dataset.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {
    "_cell_guid": "b1076dfc-b9ad-4769-8c92-a6c4dae69d19",
    "_uuid": "8f2839f25d086af736a60e9eeb907d3b93b6e0e5"
   },
   "source": [
    "## Naive Bayes (generative) model\n",
    "\n",
    "Naive Bayes model predicts the likelihood of an event based on the evidence present in the test dataset. \n",
    "\n",
    "**Conditional probability and Bayes' rule:**  \n",
    "\n",
    "$$ P(A|B) = \\frac{P(A \\cap B)}{P(B)} = \\frac{P(A) P(B|A)}{P(B)}  $$ \n",
    "\n",
    "Three types of Naive Bayes model:\n",
    "1. Multinomial (categorical or continuos, discrete frequency)\n",
    "2. Bernoulli (binary features)\n",
    "3. Gaussian (continuous, normally distributed)\n",
    "\n",
    "**Learning with practical dataset:**\n",
    "Here we fit each class (independently) with a model. Say we have two classes with one dimensional probability distributions $P_1(x)$ and $P_2(x)$. \n",
    "\n",
    "Let's say our training set has $\\pi_1$ fraction of class one and $\\pi_2$ fraction of class two ($\\pi_1 + \\pi_2 = 1$). \n",
    "\n",
    "Now for a test point (x), we predict its class for which $\\pi_iP_i(x)$ is maximum. Note that $\\pi_i$ is determined based on our training dataset. \n",
    "\n",
    "The dataset is available at <https://archive.ics.uci.edu/ml/datasets/wine> or can be imported from scikit-learn datasets module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "_cell_guid": "79c7e3d0-c299-4dcb-8224-4455121ee9b0",
    "_uuid": "d629ff2d2480ee46fbb7e2d37f6b5fab8052498a"
   },
   "outputs": [],
   "source": [
    "# load python packages\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "from sklearn.datasets import load_wine\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"figure.figsize\"] = (8, 6)\n",
    "plt.rcParams[\"font.size\"] = 16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alcohol</th>\n",
       "      <th>malic_acid</th>\n",
       "      <th>ash</th>\n",
       "      <th>alcalinity_of_ash</th>\n",
       "      <th>magnesium</th>\n",
       "      <th>total_phenols</th>\n",
       "      <th>flavanoids</th>\n",
       "      <th>nonflavanoid_phenols</th>\n",
       "      <th>proanthocyanins</th>\n",
       "      <th>color_intensity</th>\n",
       "      <th>hue</th>\n",
       "      <th>od280/od315_of_diluted_wines</th>\n",
       "      <th>proline</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14.23</td>\n",
       "      <td>1.71</td>\n",
       "      <td>2.43</td>\n",
       "      <td>15.6</td>\n",
       "      <td>127.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.06</td>\n",
       "      <td>0.28</td>\n",
       "      <td>2.29</td>\n",
       "      <td>5.64</td>\n",
       "      <td>1.04</td>\n",
       "      <td>3.92</td>\n",
       "      <td>1065.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.20</td>\n",
       "      <td>1.78</td>\n",
       "      <td>2.14</td>\n",
       "      <td>11.2</td>\n",
       "      <td>100.0</td>\n",
       "      <td>2.65</td>\n",
       "      <td>2.76</td>\n",
       "      <td>0.26</td>\n",
       "      <td>1.28</td>\n",
       "      <td>4.38</td>\n",
       "      <td>1.05</td>\n",
       "      <td>3.40</td>\n",
       "      <td>1050.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13.16</td>\n",
       "      <td>2.36</td>\n",
       "      <td>2.67</td>\n",
       "      <td>18.6</td>\n",
       "      <td>101.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.24</td>\n",
       "      <td>0.30</td>\n",
       "      <td>2.81</td>\n",
       "      <td>5.68</td>\n",
       "      <td>1.03</td>\n",
       "      <td>3.17</td>\n",
       "      <td>1185.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>14.37</td>\n",
       "      <td>1.95</td>\n",
       "      <td>2.50</td>\n",
       "      <td>16.8</td>\n",
       "      <td>113.0</td>\n",
       "      <td>3.85</td>\n",
       "      <td>3.49</td>\n",
       "      <td>0.24</td>\n",
       "      <td>2.18</td>\n",
       "      <td>7.80</td>\n",
       "      <td>0.86</td>\n",
       "      <td>3.45</td>\n",
       "      <td>1480.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.24</td>\n",
       "      <td>2.59</td>\n",
       "      <td>2.87</td>\n",
       "      <td>21.0</td>\n",
       "      <td>118.0</td>\n",
       "      <td>2.80</td>\n",
       "      <td>2.69</td>\n",
       "      <td>0.39</td>\n",
       "      <td>1.82</td>\n",
       "      <td>4.32</td>\n",
       "      <td>1.04</td>\n",
       "      <td>2.93</td>\n",
       "      <td>735.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   alcohol  malic_acid   ash  alcalinity_of_ash  magnesium  total_phenols  \\\n",
       "0    14.23        1.71  2.43               15.6      127.0           2.80   \n",
       "1    13.20        1.78  2.14               11.2      100.0           2.65   \n",
       "2    13.16        2.36  2.67               18.6      101.0           2.80   \n",
       "3    14.37        1.95  2.50               16.8      113.0           3.85   \n",
       "4    13.24        2.59  2.87               21.0      118.0           2.80   \n",
       "\n",
       "   flavanoids  nonflavanoid_phenols  proanthocyanins  color_intensity   hue  \\\n",
       "0        3.06                  0.28             2.29             5.64  1.04   \n",
       "1        2.76                  0.26             1.28             4.38  1.05   \n",
       "2        3.24                  0.30             2.81             5.68  1.03   \n",
       "3        3.49                  0.24             2.18             7.80  0.86   \n",
       "4        2.69                  0.39             1.82             4.32  1.04   \n",
       "\n",
       "   od280/od315_of_diluted_wines  proline  \n",
       "0                          3.92   1065.0  \n",
       "1                          3.40   1050.0  \n",
       "2                          3.17   1185.0  \n",
       "3                          3.45   1480.0  \n",
       "4                          2.93    735.0  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = load_wine()\n",
    "df = pd.DataFrame(data.data, columns=data.feature_names)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 178 entries, 0 to 177\n",
      "Data columns (total 13 columns):\n",
      " #   Column                        Non-Null Count  Dtype  \n",
      "---  ------                        --------------  -----  \n",
      " 0   alcohol                       178 non-null    float64\n",
      " 1   malic_acid                    178 non-null    float64\n",
      " 2   ash                           178 non-null    float64\n",
      " 3   alcalinity_of_ash             178 non-null    float64\n",
      " 4   magnesium                     178 non-null    float64\n",
      " 5   total_phenols                 178 non-null    float64\n",
      " 6   flavanoids                    178 non-null    float64\n",
      " 7   nonflavanoid_phenols          178 non-null    float64\n",
      " 8   proanthocyanins               178 non-null    float64\n",
      " 9   color_intensity               178 non-null    float64\n",
      " 10  hue                           178 non-null    float64\n",
      " 11  od280/od315_of_diluted_wines  178 non-null    float64\n",
      " 12  proline                       178 non-null    float64\n",
      "dtypes: float64(13)\n",
      "memory usage: 18.2 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's consider one feature (Alcohol) and plot it for the first category\n",
    "cat1 = df.loc[data['target']==0]\n",
    "plt.hist(cat1[\"alcohol\"], density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's fit it with Gaussian distribution\n",
    "mu = np.mean(cat1[\"alcohol\"])                # mean\n",
    "var = np.var(cat1[\"alcohol\"])                # variance\n",
    "std = np.sqrt(var)                           # standard deviation\n",
    "\n",
    "x_axis = np.linspace(mu - 3*std, mu + 3*std, 1000)\n",
    "plt.plot(x_axis, norm.pdf(x_axis,mu,std), 'r', lw=2)\n",
    "plt.hist(cat1[\"alcohol\"], density=True)\n",
    "plt.xlabel('Alcohol content')\n",
    "plt.ylabel('Probability density')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We fit probabilty distribution ($P_i$) for each category. The probability of each category is simply the $\\pi_i$ (frequency of that category)/(total sample size) in the training dataset. Now for a given new data, we simply calculate $\\pi_i P_i$, and choose the label for which it is maximum. \n",
    "\n",
    "Now we will do the same using scikit learn modules. Where we will use all the predictor variable in the data.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat1 = df.loc[data['target']==0]\n",
    "cat2 = df.loc[data['target']==1]\n",
    "cat3 = df.loc[data['target']==2]\n",
    "\n",
    "mu = np.mean(cat1[\"alcohol\"])\n",
    "var = np.var(cat1[\"alcohol\"])\n",
    "std = np.sqrt(var)\n",
    "\n",
    "mu2 = np.mean(cat2[\"alcohol\"])\n",
    "var2 = np.var(cat2[\"alcohol\"])\n",
    "std2 = np.sqrt(var2)\n",
    "\n",
    "mu3 = np.mean(cat3[\"alcohol\"])\n",
    "var3 = np.var(cat3[\"alcohol\"])\n",
    "std3 = np.sqrt(var3)\n",
    "\n",
    "x_axis = np.linspace(mu - 3*std, mu + 3*std, 1000)\n",
    "x_axis2 = np.linspace(mu2 - 3*std2, mu2 + 3*std2, 1000)\n",
    "x_axis3 = np.linspace(mu3 - 3*std3, mu3 + 3*std3, 1000)\n",
    "plt.plot(x_axis, norm.pdf(x_axis, mu, std), lw=2, label=\"cat1\")\n",
    "plt.plot(x_axis2, norm.pdf(x_axis2, mu2, std2), lw=2, label=\"cat2\")\n",
    "plt.plot(x_axis3, norm.pdf(x_axis3, mu3, std3), lw=2, label=\"cat3\")\n",
    "\n",
    "plt.xlabel('Alcohol content')\n",
    "plt.ylabel('Probability density')\n",
    "plt.legend(frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first do a train test split of our data\n",
    "X, X_test, y, y_test = train_test_split(df, data['target'], test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 40]\n",
      " [ 1 49]\n",
      " [ 2 35]]\n"
     ]
    }
   ],
   "source": [
    "# check that we have sufficient data of each wine category \n",
    "unique, counts = np.unique(y, return_counts=True)\n",
    "print(np.asarray((unique, counts)).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 19]\n",
      " [ 1 22]\n",
      " [ 2 13]]\n"
     ]
    }
   ],
   "source": [
    "print(np.asarray(np.unique(y_test, return_counts=True)).T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GaussNB = GaussianNB()\n",
    "GaussNB.fit(X, y)\n",
    "GaussNB.predict([X_test.iloc[4]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 2, 1, 0, 1])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9444444444444444"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GaussNB.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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