33_logistic_regression-full.ipynb

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   "source": [
    "# ICS 434: DATA SCIENCE FUNDAMENTALS\n",
    "\n",
    "## Logistic Regression\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Announcements\n",
    "\n",
    "* Homework assignment #5\n",
    "   * Due: **Thursday, April 27, 11:59 PM**\n",
    "   * Refer to the `Homework submission guidelines` announcement in Laulima for preparing and submitting your homework."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## Slide Credits\n",
    "\n",
    "Most of these slides were taken from Mahdi Belcaid."
   ]
  },
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   "execution_count": 1,
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   "source": [
    "# %load ../standard_import.txt\n",
    "from IPython.display import Image\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "%matplotlib inline"
   ]
  },
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   "source": [
    "### Logistic Regrssion\n",
    "\n",
    "* The linear regression model discussed assumes response is quantitative\n",
    "* But in many situations, the response variable is instead qualitative\n",
    "\n",
    "* Logistic Regression for the outcome to be qualitative (or categorical)\n",
    "\n",
    "  * The main difference between Linear versus logistic regression is in the type of outcomes predicted   \n",
    "\n",
    "* Email: SPAM vs. HAM\n",
    "* An individual will get a disease or not\n",
    "* Etc.\n",
    "\n",
    "* Logistic Regression is one among many solutions to classification\n"
   ]
  },
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   "source": [
    "### Classification\n",
    "\n",
    "* Classification takes a set of inputs and assigns them to a qualitative outcome \n",
    " * A qualitative outcome is one that takes values in a set of possible categories \n",
    " \n",
    "* Often, we are interested in predicting the probability that an input belongs to each category\n",
    "  * We can then take the assignment with the highest probability\n",
    "  * I.e., more relevant to say a computer is infected with 0.99 probability or 0.52 probability than just infected"
   ]
  },
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   "source": [
    "### Classes of Logistic Regression\n",
    "\n",
    "* There are two types of logistic regression into:\n",
    "  * Simple or binary logistic regression\n",
    "  * Multiclass logistic regression\n",
    "* We focus on (binary) logistic regression\n",
    "  * Ease to generalize to more than two classes"
   ]
  },
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   "source": [
    "### Dataset \n",
    "\n",
    "* People who default on their credit card paymment (brown marks) versus those who don't (blue circles)\n",
    "\n",
    "<img src=\"images/classification_1.png\" alt=\"drawing\" style=\"width:1000px;\"/>\n"
   ]
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   "source": [
    "### Justification for logistic regression\n",
    "\n",
    "- Can we use linear regression to determine whether a client defaults on credit card payment? How?\n",
    "- One possible way is to assign given output to classes (say 0 and 1) and use linear regression to generate value that span the 0,1 range\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "    \\begin{array}{ll}\n",
    "        1 & \\mbox{if default} \\\\\n",
    "        0 & \\mbox{otherwise}\n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "### Using Linear in Classification\n",
    "\n",
    "<img src=\"images/regression_1.png\" alt=\"drawing\" style=\"width:500px;\"/>\n",
    "\n"
   ]
  },
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   "source": [
    "### Using Linear in Classification - Cont'd\n",
    "\n",
    "\n",
    "* Remember that linear regression predicts continuous values\n",
    "* We can say then that: \n",
    "  * Any value that our linear regression predicts as above a certain threshold represents class 1\n",
    "  * Any value that our linear regression predicts below a certain threshold represents class 0\n",
    "* 0.5 is a reasonable threshold as it sits exactly in the middle classes 0 and 1\n",
    "  "
   ]
  },
  {
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   "metadata": {
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   "source": [
    "### Using Linear in Classification - Model\n",
    "\n",
    "<img src=\"images/regression_2.png\" alt=\"drawing\" style=\"width:500px;\"/>\n"
   ]
  },
  {
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   "metadata": {
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   "source": [
    "### Using Linear in Classification - Prediction\n",
    "\n",
    "<img src=\"images/regression_3.png\" alt=\"drawing\" style=\"width:800px;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
   },
   "source": [
    "### Using Linear in Classification - Prediction Regions\n",
    "\n",
    "<img src=\"images/regression_4.png\" alt=\"drawing\" style=\"width:800px;\"/>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    }
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   "source": [
    "### Inconvenients of Using Linear Regression\n",
    "\n",
    "* Problems with \"hacking\" linear regression for classification\n",
    "\n",
    "\n",
    "* The regression line is sensitive to the data\n",
    "  * outliers can drastically change the intersection point of the threshold on the line\n",
    "  \n",
    "\n",
    "* Predicted value can be much smaller than 0 or much larger than 1\n",
    "  * Impossible to interpret as a probability"
   ]
  },
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   },
   "source": [
    "<img src=\"images/regression_5.png\" alt=\"drawing\" style=\"width:500px;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "## Logistic Regression\n",
    "\n",
    "* A very simple yet popular method for classification\n",
    "\n",
    "* Constrains the predicted value to be between 0 and 1\n",
    "  * Can be interpreted as a probability for a class\n",
    "  \n",
    "Use the logistic, or sigmoid function, to model the separation between the classes\n",
    "\n",
    "\n",
    "$$ g(x) = \\frac{1}{1+e^-(\\beta_0 + \\beta_1~x)}$$\n",
    "\n"
   ]
  },
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   "source": [
    "## Logistic Regression\n",
    "\n",
    "* Assuming $\\beta_0=0$ and $\\beta_1=1$\n",
    "\n",
    "<img src=\"images/logistic_regression.png\" alt=\"drawing\" style=\"width:700px;\"/>\n",
    "\n",
    "* The logistic function g(x) provides $prob(y=1~|~x, \\beta_1, \\beta_2)$\n",
    "  * The probability that a value x is 1.\n"
   ]
  },
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.arange(-10, 10, 0.05)\n",
    "y_axis = 1 / (1 + np.e**-x_axis)\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.plot(x_axis, y_axis)\n",
    "plt.axhline(0.5, linestyle=\"--\", color='r', alpha=0.2)\n",
    "plt.axvline(0, linestyle=\"--\", color='k', alpha=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Parameters of the Logstic \n",
    "- As with the linear regression, we assumed that the params of the model $\\beta_0$ and $\\beta_1$ can be anything"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.38389653e-87, 3.76182078e-87, 1.02256891e-86, 2.77963048e-86,\n",
       "       7.55581902e-86, 2.05388455e-85, 5.58303706e-85, 1.51762682e-84,\n",
       "       4.12533740e-84, 1.12138297e-83, 3.04823495e-83, 8.28596168e-83,\n",
       "       2.25235791e-82, 6.12254357e-82, 1.66427989e-81, 4.52398179e-81,\n",
       "       1.22974575e-80, 3.34279552e-80, 9.08666032e-80, 2.47001036e-79,\n",
       "       6.71418429e-79, 1.82510451e-78, 4.96114844e-78, 1.34857996e-77,\n",
       "       3.66582041e-77, 9.96473301e-77, 2.70869527e-76, 7.36299712e-76,\n",
       "       2.00147013e-75, 5.44055988e-75, 1.47889751e-74, 4.02006022e-74,\n",
       "       1.09276566e-73, 2.97044505e-73, 8.07450679e-73, 2.19487851e-72,\n",
       "       5.96629836e-72, 1.62180804e-71, 4.40853133e-71, 1.19836306e-70,\n",
       "       3.25748853e-70, 8.85477188e-70, 2.40697655e-69, 6.54284062e-69,\n",
       "       1.77852848e-68, 4.83454164e-68, 1.31416467e-67, 3.57226994e-67,\n",
       "       9.71043646e-67, 2.63957030e-66, 7.17509597e-66, 1.95039330e-65,\n",
       "       5.30171867e-65, 1.44115655e-64, 3.91746966e-64, 1.06487866e-63,\n",
       "       2.89464031e-63, 7.86844816e-63, 2.13886596e-62, 5.81404049e-62,\n",
       "       1.58042006e-61, 4.29602713e-61, 1.16778125e-60, 3.17435855e-60,\n",
       "       8.62880116e-60, 2.34555134e-59, 6.37586958e-59, 1.73314104e-58,\n",
       "       4.71116580e-58, 1.28062764e-57, 3.48110684e-57, 9.46262947e-57,\n",
       "       2.57220937e-56, 6.99199000e-56, 1.90061994e-55, 5.16642063e-55,\n",
       "       1.40437873e-54, 3.81749719e-54, 1.03770332e-53, 2.82077009e-53,\n",
       "       7.66764807e-53, 2.08428284e-52, 5.66566818e-52, 1.54008828e-51,\n",
       "       4.18639400e-51, 1.13797987e-50, 3.09335001e-50, 8.40859712e-50,\n",
       "       2.28569368e-49, 6.21315959e-49, 1.68891188e-48, 4.59093847e-48,\n",
       "       1.24794646e-47, 3.39227019e-47, 9.22114642e-47, 2.50656748e-46,\n",
       "       6.81355682e-46, 1.85211677e-45, 5.03457536e-45, 1.36853947e-44,\n",
       "       3.72007598e-44, 1.01122149e-43, 2.74878501e-43, 7.47197234e-43,\n",
       "       2.03109266e-42, 5.52108228e-42, 1.50078576e-41, 4.07955867e-41,\n",
       "       1.10893902e-40, 3.01440879e-40, 8.19401262e-40, 2.22736356e-39,\n",
       "       6.05460190e-39, 1.64581143e-38, 4.47377931e-38, 1.21609930e-37,\n",
       "       3.30570063e-37, 8.98582594e-37, 2.44260074e-36, 6.63967720e-36,\n",
       "       1.80485139e-35, 4.90609473e-35, 1.33361482e-34, 3.62514092e-34,\n",
       "       9.85415469e-34, 2.67863696e-33, 7.28129018e-33, 1.97925988e-32,\n",
       "       5.38018616e-32, 1.46248623e-31, 3.97544974e-31, 1.08063928e-30,\n",
       "       2.93748211e-30, 7.98490425e-30, 2.17052201e-29, 5.90009054e-29,\n",
       "       1.60381089e-28, 4.35961000e-28, 1.18506486e-27, 3.22134029e-27,\n",
       "       8.75651076e-27, 2.38026641e-26, 6.47023493e-26, 1.75879220e-25,\n",
       "       4.78089288e-25, 1.29958143e-24, 3.53262857e-24, 9.60268005e-24,\n",
       "       2.61027907e-23, 7.09547416e-23, 1.92874985e-22, 5.24288566e-22,\n",
       "       1.42516408e-21, 3.87399763e-21, 1.05306174e-20, 2.86251858e-20,\n",
       "       7.78113224e-20, 2.11513104e-19, 5.74952226e-19, 1.56288219e-18,\n",
       "       4.24835426e-18, 1.15482242e-17, 3.13913279e-17, 8.53304763e-17,\n",
       "       2.31952283e-16, 6.30511676e-16, 1.71390843e-15, 4.65888615e-15,\n",
       "       1.26641655e-14, 3.44247711e-14, 9.35762297e-14, 2.54366565e-13,\n",
       "       6.91440011e-13, 1.87952882e-12, 5.10908903e-12, 1.38879439e-11,\n",
       "       3.77513454e-11, 1.02618796e-10, 2.78946809e-10, 7.58256043e-10,\n",
       "       2.06115362e-09, 5.60279644e-09, 1.52299797e-08, 4.13993772e-08,\n",
       "       1.12535175e-07, 3.05902321e-07, 8.31528719e-07, 2.26032941e-06,\n",
       "       6.14421235e-06, 1.67017008e-05, 4.53999298e-05, 1.23409804e-04,\n",
       "       3.35462628e-04, 9.11881966e-04, 2.47875218e-03, 6.73794700e-03,\n",
       "       1.83156389e-02, 4.97870684e-02, 1.35335283e-01, 3.67879441e-01,\n",
       "       1.00000000e+00, 2.71828183e+00, 7.38905610e+00, 2.00855369e+01,\n",
       "       5.45981500e+01, 1.48413159e+02, 4.03428793e+02, 1.09663316e+03,\n",
       "       2.98095799e+03, 8.10308393e+03, 2.20264658e+04, 5.98741417e+04,\n",
       "       1.62754791e+05, 4.42413392e+05, 1.20260428e+06, 3.26901737e+06,\n",
       "       8.88611052e+06, 2.41549528e+07, 6.56599691e+07, 1.78482301e+08,\n",
       "       4.85165195e+08, 1.31881573e+09, 3.58491285e+09, 9.74480345e+09,\n",
       "       2.64891221e+10, 7.20048993e+10, 1.95729609e+11, 5.32048241e+11,\n",
       "       1.44625706e+12, 3.93133430e+12, 1.06864746e+13, 2.90488497e+13,\n",
       "       7.89629602e+13, 2.14643580e+14, 5.83461743e+14, 1.58601345e+15,\n",
       "       4.31123155e+15, 1.17191424e+16, 3.18559318e+16, 8.65934004e+16,\n",
       "       2.35385267e+17, 6.39843494e+17, 1.73927494e+18, 4.72783947e+18,\n",
       "       1.28516001e+19, 3.49342711e+19, 9.49611942e+19, 2.58131289e+20,\n",
       "       7.01673591e+20, 1.90734657e+21, 5.18470553e+21, 1.40934908e+22,\n",
       "       3.83100800e+22, 1.04137594e+23, 2.83075330e+23, 7.69478527e+23,\n",
       "       2.09165950e+24, 5.68572000e+24, 1.54553894e+25, 4.20121040e+25,\n",
       "       1.14200739e+26, 3.10429794e+26, 8.43835667e+26, 2.29378316e+27,\n",
       "       6.23514908e+27, 1.69488924e+28, 4.60718663e+28, 1.25236317e+29,\n",
       "       3.40427605e+29, 9.25378173e+29, 2.51543867e+30, 6.83767123e+30,\n",
       "       1.85867175e+31, 5.05239363e+31, 1.37338298e+32, 3.73324200e+32,\n",
       "       1.01480039e+33, 2.75851345e+33, 7.49841700e+33, 2.03828107e+34,\n",
       "       5.54062238e+34, 1.50609731e+35, 4.09399696e+35, 1.11286375e+36,\n",
       "       3.02507732e+36, 8.22301271e+36, 2.23524660e+37, 6.07603023e+37,\n",
       "       1.65163626e+38, 4.48961282e+38, 1.22040329e+39, 3.31740010e+39,\n",
       "       9.01762841e+39, 2.45124554e+40, 6.66317622e+40, 1.81123908e+41,\n",
       "       4.92345829e+41, 1.33833472e+42, 3.63797095e+42, 9.88903032e+42,\n",
       "       2.68811714e+43, 7.30705998e+43, 1.98626484e+44, 5.39922761e+44,\n",
       "       1.46766223e+45, 3.98951957e+45, 1.08446386e+46, 2.94787839e+46,\n",
       "       8.01316426e+46, 2.17820388e+47, 5.92097203e+47, 1.60948707e+48,\n",
       "       4.37503945e+48, 1.18925902e+49, 3.23274119e+49, 8.78750164e+49,\n",
       "       2.38869060e+50, 6.49313426e+50, 1.76501689e+51, 4.79781333e+51,\n",
       "       1.30418088e+52, 3.54513118e+52, 9.63666567e+52, 2.61951732e+53,\n",
       "       7.12058633e+53, 1.93557604e+54, 5.26144118e+54, 1.43020800e+55,\n",
       "       3.88770841e+55, 1.05678871e+56, 2.87264955e+56, 7.80867107e+56,\n",
       "       2.12261687e+57, 5.76987086e+57, 1.56841351e+58, 4.26338995e+58,\n",
       "       1.15890954e+59, 3.15024275e+59, 8.56324762e+59, 2.32773204e+60,\n",
       "       6.32743171e+60, 1.71997426e+61, 4.67537478e+61, 1.27089863e+62,\n",
       "       3.45466066e+62, 9.39074129e+62, 2.55266814e+63, 6.93887142e+63,\n",
       "       1.88618081e+64, 5.12717102e+64, 1.39370958e+65, 3.78849543e+65,\n",
       "       1.02981983e+66, 2.79934052e+66, 7.60939648e+66, 2.06844842e+67,\n",
       "       5.62262575e+67, 1.52838814e+68, 4.15458971e+68, 1.12933457e+69,\n",
       "       3.06984964e+69, 8.34471649e+69, 2.26832912e+70, 6.16595783e+70,\n",
       "       1.67608111e+71, 4.55606083e+71, 1.23846574e+72, 3.36649891e+72,\n",
       "       9.15109281e+72, 2.48752493e+73, 6.76179381e+73, 1.83804612e+74,\n",
       "       4.99632738e+74, 1.35814259e+75, 3.69181433e+75, 1.00353918e+76,\n",
       "       2.72790232e+76, 7.41520730e+76, 2.01566233e+77, 5.47913827e+77,\n",
       "       1.48938420e+78, 4.04856601e+78, 1.10051434e+79, 2.99150814e+79,\n",
       "       8.13176221e+79, 2.21044214e+80, 6.00860471e+80, 1.63330810e+81,\n",
       "       4.43979173e+81, 1.20686052e+82, 3.28058702e+82, 8.91756007e+82,\n",
       "       2.42404415e+83, 6.58923516e+83, 1.79113982e+84, 4.86882283e+84,\n",
       "       1.32348326e+85, 3.59760050e+85, 9.77929207e+85, 2.65828719e+86])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(-(beta_0 + beta_1*x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Changing $\\beta_0$\n",
    "\n",
    "<img src=\"images/changing_beta0.png\" alt=\"drawing\" style=\"width:1500px;\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17480f0d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.axhline(0.5, linestyle=\"--\", color='r', alpha=0.2)\n",
    "plt.axvline(0, linestyle=\"--\", color='k', alpha=0.2)\n",
    "x = np.arange(-10, 10, 0.05)\n",
    "\n",
    "beta_0, beta_1 = (0, 1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (-5, 1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (5, 1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "beta_0, beta_1 = (0, -1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (-5, -1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (5, -1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Changing $\\beta_1$\n",
    "\n",
    "<img src=\"images/logistic_beta_1.png\" alt=\"drawing\" style=\"width:1500px;\"/>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x177759520>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.axhline(0.5, linestyle=\"--\", color='r', alpha=0.2)\n",
    "plt.axvline(0, linestyle=\"--\", color='k', alpha=0.2)\n",
    "x = np.arange(-10, 10, 0.05)\n",
    "\n",
    "beta_0, beta_1 = (0, 0.6) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (0, 1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (0, 20) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "beta_0, beta_1 = (0, -0.6) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (0, -1) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "beta_0, beta_1 = (0, -20) \n",
    "y = 1 / (1 + np.e **-(beta_0 + beta_1*x))\n",
    "plt.plot(x, y, label = r'$\\beta_0 = {}, \\beta_1 = {}$'.format(beta_0, beta_1))\n",
    "\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x177996910>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.arange(-10, 10, 0.05)\n",
    "y_axis = 1 / (1 + np.e**-x_axis)\n",
    "plt.figure(figsize=(12,6))\n",
    "plt.plot([2.5], [1 / (1 + np.e**-2.5)], 'or', markersize=12)\n",
    "\n",
    "plt.plot(x_axis, y_axis)\n",
    "plt.axhline(0.5, linestyle=\"--\", color='k', alpha=0.2)\n",
    "plt.axvline(0, linestyle=\"--\", color='k', alpha=0.2)\n",
    "\n",
    "plt.axhline(1 / (1 + np.e**-2.5), linestyle=\"--\", color='r', alpha=0.2)\n",
    "plt.axvline(2.5, linestyle=\"--\", color='r', alpha=0.2)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Fitting the Model: Linear Regression Parallel\n",
    "\n",
    "* For the Linear regression, we used the data to parameterize the model\n",
    "  * We trained the model to find the line that minimizes the RSS \n",
    "  * I.e, among all possible lines, the one selected has the smallest sum of squared residuals\n",
    "  \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Fitting the Model\n",
    "\n",
    "* In binary logistic regression, the outcomes  are 0 and 1, and the predictions are also either 0 or 1\n",
    "\n",
    "* One trivial approach would consist in identifying the sigmoid function that minimizes the mispredictions\n",
    "*  Using the same method as in linear regression, we could describe the function as:\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} \\sum_1^n (g(x) - y)\n",
    "$$\n",
    "\n",
    "* Unfortunately, this function is not convex \n",
    "\n",
    "  *  Does guarantee that the function will converge to the global minimum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Fitting the Model- Cont'd\n",
    "\n",
    "\n",
    "- Instead, given some tuple (beta_0 and beta_1), the following convex function is commonly used to compute the cost\n",
    "\n",
    "$$\n",
    "    cost(g(x),y) = \\left\\{\n",
    "    \\begin{array}{ll}\n",
    "        -log(g(x)) & \\mbox{ if }  y = 1 \\\\\n",
    "        -log(1 - g(x)) & \\mbox{ if }  y = 0 \\\\\n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "* Remember that $g(x)$ is simply the probability that the class is 1\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Cost Function Explained - $y=1$\n",
    "\n",
    "$$\n",
    "        -log(g(x)) \\mbox{ if }  y = 1\n",
    "$$\n",
    "\n",
    "* For $y = 1$\n",
    "  - If the prediction is also 1, then we incur no cost \n",
    "  - If the prediction is 0, then we are incurring an infinite cost "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 3.0)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.arange(0.000001, 1.1, 0.05)\n",
    "y_axis = - np.log(x_axis)\n",
    "plt.plot(x_axis, y_axis)\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Cost Function Explained - $y=1$\n",
    "\n",
    "$$\n",
    "        -log(1 - g_(x)) \\mbox{ if }  y = 0 \\\\\n",
    "$$\n",
    "- for $y = 0$\n",
    "  - If the prediction is also 0, then we incur no cost \n",
    "  - If the prediction is 1, then we are incurring an infinite cost \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 3.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_axis = np.arange(0, 0.9999999, 0.05)\n",
    "y_axis = - np.log(1 - x_axis)\n",
    "plt.plot(x_axis, y_axis)\n",
    "plt.xlim(0,1)\n",
    "plt.ylim(0,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Training\n",
    "\n",
    "- Therefore, by averaging the cost over all instances in the data, we end up with the parameters ($\\beta$s) that best fit the data\n",
    "\n",
    "- Thus for a dataset of size $n$, we pick the tuple $\\beta$ of params which minimizes:\n",
    "\n",
    "$$\n",
    "\\sum_{\\forall x}cost(g(x)_{\\beta},y)~~/~~n\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Prediction\n",
    "\n",
    "* Use the parameters $\\beta$ identified in the training to predict the probabality of true using\n",
    "$$\n",
    "p(y=1| x, \\beta_0,\\beta_1) = g(x) = \\frac{1}{1+e^{\\beta_0+\\beta_1~x}}\n",
    "$$\n",
    " *  Probabolty of False is merely $1- p(y=1| x, \\beta_0,\\beta_1)$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mahdi/miniconda3/lib/python3.8/site-packages/openpyxl/styles/stylesheet.py:226: UserWarning: Workbook contains no default style, apply openpyxl's default\n",
      "  warn(\"Workbook contains no default style, apply openpyxl's default\")\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>default</th>\n",
       "      <th>student</th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>No</td>\n",
       "      <td>729.526495</td>\n",
       "      <td>44361.625074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>817.180407</td>\n",
       "      <td>12106.134700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>1073.549164</td>\n",
       "      <td>31767.138947</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>529.250605</td>\n",
       "      <td>35704.493935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>785.655883</td>\n",
       "      <td>38463.495879</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0 default student      balance        income\n",
       "0           1      No      No   729.526495  44361.625074\n",
       "1           2      No     Yes   817.180407  12106.134700\n",
       "2           3      No      No  1073.549164  31767.138947\n",
       "3           4      No      No   529.250605  35704.493935\n",
       "4           5      No      No   785.655883  38463.495879"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_excel(\"data/Default.xlsx\")\n",
    "data.head()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>default</th>\n",
       "      <th>student</th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
       "      <th>encoded_default</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>729.526495</td>\n",
       "      <td>44361.625074</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>817.180407</td>\n",
       "      <td>12106.134700</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>1073.549164</td>\n",
       "      <td>31767.138947</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>529.250605</td>\n",
       "      <td>35704.493935</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>785.655883</td>\n",
       "      <td>38463.495879</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0 default student      balance        income  encoded_default\n",
       "0           1      No      No   729.526495  44361.625074                0\n",
       "1           2      No     Yes   817.180407  12106.134700                0\n",
       "2           3      No      No  1073.549164  31767.138947                0\n",
       "3           4      No      No   529.250605  35704.493935                0\n",
       "4           5      No      No   785.655883  38463.495879                0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "data[\"encoded_default\"] = data[\"default\"].map({\"No\":0, \"Yes\":1})\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Logistic Regression with `sklearn`\n",
    "\n",
    "* Using statsmodels, we can infer the values of \\beta_0 and \\beta_1 such that\n",
    "\n",
    "$$\n",
    "    default = \\frac{1}{1 + e^{-(\\beta_o + \\beta_1 ~ balance})} + \\epsilon_x\n",
    "$$\n",
    "\n",
    "* Similar  to the regression, $\\epsilon$ is the noise component\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        729.526495\n",
       "1        817.180407\n",
       "2       1073.549164\n",
       "3        529.250605\n",
       "4        785.655883\n",
       "           ...     \n",
       "9995     711.555020\n",
       "9996     757.962918\n",
       "9997     845.411989\n",
       "9998    1569.009053\n",
       "9999     200.922183\n",
       "Name: balance, Length: 10000, dtype: float64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.loc[:, \"balance\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=100000.0)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "logreg = LogisticRegression(C=1e5, solver='lbfgs')\n",
    "#  We use the limited memory Broyden–Fletcher–Goldfarb–Shanno optimization algorithm\n",
    "\n",
    "X = data[\"balance\"].values.reshape(-1,1) \n",
    "Y = data[\"encoded_default\"].values \n",
    "logreg.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0.00549892]]), array([-10.65132867]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logreg.coef_, logreg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model Interpretation - Balance\n",
    "\n",
    "\n",
    "$$\n",
    "    P(default=1| x, \\beta_0, \\beta_1) \\approx \\frac{1}{1 + e^{10 - 0.0005 ~ balance}}\n",
    "$$\n",
    "\n",
    "- Note that $\\beta_1$ reflects the units, which in this case is dollar\n",
    "\n",
    "- Therefore, an increase of a balnce of $1, increases the probability of defaulting by \n",
    "  \n",
    "$$\n",
    "    P(default=1| x=1, \\beta_0=-10.65, \\beta_1=0.0055) \\approx \\frac{1}{1 + e^{10 - 0.0005 * 1}} = 0.000045\n",
    "$$\n",
    "\n",
    "- An increase of a balnce of $2,000, increases the probability of defaulting by \n",
    "\n",
    "$$\n",
    "    P(default=1| x=2,000, \\beta_0=-10.65, \\beta_1=0.0055) \\approx \\frac{1}{1 + e^{10 - 0.0005 * 2,000}} \\approx 0.5\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Multiple Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "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>Unnamed: 0</th>\n",
       "      <th>default</th>\n",
       "      <th>student</th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
       "      <th>encoded_default</th>\n",
       "      <th>encoded_student</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>729.526495</td>\n",
       "      <td>44361.625074</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>817.180407</td>\n",
       "      <td>12106.134700</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>1073.549164</td>\n",
       "      <td>31767.138947</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>529.250605</td>\n",
       "      <td>35704.493935</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>785.655883</td>\n",
       "      <td>38463.495879</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0 default student      balance        income  encoded_default  \\\n",
       "0           1      No      No   729.526495  44361.625074                0   \n",
       "1           2      No     Yes   817.180407  12106.134700                0   \n",
       "2           3      No      No  1073.549164  31767.138947                0   \n",
       "3           4      No      No   529.250605  35704.493935                0   \n",
       "4           5      No      No   785.655883  38463.495879                0   \n",
       "\n",
       "   encoded_student  \n",
       "0                0  \n",
       "1                1  \n",
       "2                0  \n",
       "3                0  \n",
       "4                0  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"encoded_student\"] = data[\"student\"].map({\"No\":0, \"Yes\":1})\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[0.40489192]]), array([-3.50412908]))"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data[\"encoded_student\"].values.reshape(-1,1)\n",
    "y = data[\"encoded_default\"].values\n",
    "\n",
    "logreg.fit(X, Y)\n",
    "logreg.coef_, logreg.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model Interpretation - Student Status\n",
    "\n",
    "\n",
    "$$\n",
    "    P(default=1| x, \\beta_0, \\beta_1) \\approx \\frac{1}{1 + e^{-3.5 - 0.4 ~ student}}\n",
    "$$\n",
    "\n",
    "- the probability of a student defaulting is \n",
    "\n",
    "$$\n",
    "    P(default=1| x=1, \\beta_0=-3.5, \\beta_1=0.4) \\approx \\frac{1}{1 + e^{3.5 - 0.4 ~ 1}} \\approx 0.04\n",
    "$$\n",
    "\n",
    "\n",
    "- the probability of a non student defaulting is \n",
    "\n",
    "$$\n",
    "    P(default=1 | x=0, \\beta_0=-3.5, \\beta_1=0.4) \\approx \\frac{1}{1 + e^{-3.5 - 0.4 ~ student}} \\approx 0.02\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Multiple Logistic Regression \n",
    "\n",
    "* As we added more relevant variables, the logistic regression model becomes more discriminative\n",
    "\n",
    "  * We could combine  into a single regression the student status, total debt, age, income, number of recent credit applications, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 0.0057381 , -0.71487752]]), array([-10.74949566]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data[['balance', 'encoded_student']]\n",
    "\n",
    "y = data[\"encoded_default\"].values\n",
    "\n",
    "logreg.fit(X, Y)\n",
    "\n",
    "logreg.coef_, logreg.intercept_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "$$\n",
    "    P(default=1| x, \\beta_0, \\beta_1) \\approx \\frac{1}{1 + e^{10  - 0.0005 balance + 0.71 ~ student}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mahdi/anaconda3/lib/python3.6/site-packages/seaborn/categorical.py:462: FutureWarning: remove_na is deprecated and is a private function. Do not use.\n",
      "  box_data = remove_na(group_data)\n"
     ]
    },
    {
     "data": {
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3fpExiMD+vgynpkqNgH0x0XNhrsqOfHpZcbXSvqqVlMy1pcUowX/u49i7P4e7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\noR24l0vb9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9SPaQc+lUkdej0O0MZyaZSxFHlcGmWsxgEP9Bo3qIODhGvTgmN16+CraTaT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\nty0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oG6OCzaSk6Xv4ShIoSW9YOVDFhf8ORQU2R2iL1oXDpwP66r+kzPsQzKGTddaLiG73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\n2L5/ozG/BvwawEc+8pGyRuubjErleNlZ7zZKgXUf3E/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x125dff358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib as mpl\n",
    "import seaborn as sns\n",
    "\n",
    "fig = plt.figure(figsize=(12,5))\n",
    "gs = mpl.gridspec.GridSpec(1, 4)\n",
    "ax1 = plt.subplot(gs[0,:-2])\n",
    "ax2 = plt.subplot(gs[0,-2])\n",
    "ax3 = plt.subplot(gs[0,-1])\n",
    "\n",
    "# Take a fraction of the samples where target value (default) is 'no'\n",
    "df_no = data[data[\"encoded_default\"] == 0].sample(frac=0.15)\n",
    "# Take all samples  where target value is 'yes'\n",
    "df_yes = data[data[\"encoded_default\"]  == 1]\n",
    "df_ = df_no.append(df_yes)\n",
    "\n",
    "ax1.scatter(df_[df_.default == 'Yes'].balance, df_[df_.default == 'Yes'].income, s=40, c='orange', marker='+',\n",
    "            linewidths=1)\n",
    "ax1.scatter(df_[df_.default == 'No'].balance, df_[df_.default == 'No'].income, s=40, marker='o', linewidths='1',\n",
    "            edgecolors='lightblue', facecolors='white', alpha=.6)\n",
    "\n",
    "ax1.set_ylim(ymin=0)\n",
    "ax1.set_ylabel('Income')\n",
    "ax1.set_xlim(xmin=-100)\n",
    "ax1.set_xlabel('Balance')\n",
    "\n",
    "c_palette = {'No':'lightblue', 'Yes':'orange'}\n",
    "sns.boxplot('default', 'balance', data=data, orient='v', ax=ax2, palette=c_palette)\n",
    "sns.boxplot('default', 'income', data=data, orient='v', ax=ax3, palette=c_palette)\n",
    "gs.tight_layout(plt.gcf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Inspecting the Contribution of Income\n",
    "\n",
    "- The plot above did not indicate that income is useful for separating the data\n",
    "\n",
    "  - What does the logistic regression model say about the contribution of the variable income?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-2.67640576e+00,  4.91924349e-03, -1.00364967e-04,\n",
       "         -3.52829225e+00]]), array([-2.67640576]))"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = sm.add_constant(data[['balance', 'income', 'encoded_student']])\n",
    "\n",
    "y = data[\"encoded_default\"].values\n",
    "\n",
    "logreg.fit(X, Y)\n",
    "\n",
    "logreg.coef_, logreg.intercept_\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Categortical Variables as Predictors\n",
    "\n",
    "* A Categorical variable (sometimes called a nominal variable) is one that has two or more categories\n",
    "\n",
    "  * categorical variables have no intrinsic ordering to the categories\n",
    "\n",
    "* For instance, car types can be encoded as electric (0), sedan (1), compact (2), SUV (3), etc...\n",
    "\n",
    "* The resulting numerical encoding does not have the same meaning as regular numerical values\n",
    "\n",
    "  * Ex.: we cannot use the encoding to compute Euclidean distance or to compute averages on features\n",
    "\n",
    "* Data values for electric 0 and sedan 1 are not more similar than those with the values 0 and 2 ('electric' and 'compact')\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### One-Hot-Encoding\n",
    "\n",
    "\n",
    "* Categorical variables are commonly encoded using attributes for each category\n",
    "\n",
    "* The value is 1 for the attribute if the instance is in that category or the value is 0 otherwise\n",
    "\n",
    "* Ex.:\n",
    "  * if a data point is of type electric vehicle 0, then its encoding would be [1,0,0,0]\n",
    "  * if a data point is in SUV 4, then its encoding would be [0,0,0,1]\n",
    "\n",
    "* etc...\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relationship Between Logistic and Linear Model\n",
    "\n",
    "We have:\n",
    "\n",
    "$$p(x) = \\frac{1}{1+e^-(\\beta_0 + \\beta_1~x)}$$\n",
    "\n",
    "or:\n",
    "\n",
    "$$p(x) = \\frac{e^{(\\beta_0 + \\beta_1~x)}}{1+e^{e(\\beta_0 + \\beta_1~x)}}$$\n",
    "\n",
    "This can be written as\n",
    "\n",
    "$$\\frac{p(x)}{1-p(x)} = e^{(\\beta_0 + \\beta_1~x)}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relationship Between Logistic and Linear Model - Cont'd\n",
    "\n",
    "\n",
    "* The ratio $\\frac{p(x)}{1-p(x)}$ is the odd ratio\n",
    "   * Takes values between 0 and $\\inf$\n",
    "   \n",
    "   \n",
    "* Say the probavility of defaulting is p(x) = 0.2, then  $\\frac{p(x)}{1-p(x)} = 1/5$\n",
    "  * So, 1 in 5 people will defautl"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Relationship Between Logistic and Linear Model - Cont'd\n",
    "\n",
    "We have that:\n",
    "    \n",
    "$$\\frac{p(x)}{1-p(x)} = e^{(\\beta_0 + \\beta_1~x)}$$\n",
    "\n",
    "By taking log on both side, we have:\n",
    "\n",
    "This can be written as\n",
    "\n",
    "$$log(\\frac{p(x)}{1-p(x)}) =(\\beta_0 + \\beta_1~x)$$\n",
    "\n",
    "* Left hand side if called log-odds or logit\n",
    "\n",
    "* Therefore, the linear model has a logit that is linear in $X$\n",
    "\n",
    "Unline in linear model, $\\beta_1$ does not correspond to the change associate in one-unit increase in X.\n"
   ]
  }
 ],
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   "file_extension": ".py",
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