logistic-regression-clearly-explained.ipynb

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    "# Logistic Regression\n",
    "\n",
    "Logistic Regression is a statistical model that is used in classification and predictive analysis. This model is also know as Logit and it is characterized by a single binary dependent variable, i. e. a variable that only can take two values, often labeled as 0 and 1. Binary values are widely udsed in statistics to model the probablity of a certain event occuring, such as the probability of a pacient being health, a tumor being malignant or not, if an email is spam or not and if a team win or loose. Therefore, Logistic Regression has a large variety of applications. In this tutorial we will present a clear explanation about logistic regression models, build from scratch a model and compare it with the scikit learn implementaion.\n",
    "\n",
    "The logistic function is defined by:\n",
    "$$ p(x) = \\dfrac{1}{1+e^{-(x-\\mu)/s}} $$\n",
    "where $\\mu$ is the midpoint of the curve ($p(\\mu)=1/2$) and $s$ a scale parameter that determines the spread of the probability distribution. This function is also called **sigmoid function**, because of its 's' shape.\n",
    "\n",
    "The logistic fuction is used to generate predictions as we will see below. Furthermore, it is interesting to write this function as \n",
    "$$ p(x) = \\dfrac{1}{1+e^{-(\\beta_0 + \\beta_1 x)}} \\,,$$ \n",
    "where $\\beta_0 = -\\mu/s$ is the intercept of the line $y = \\beta_0 + \\beta_1 x$ and $\\beta_1 = 1/s$ is its slope. The parameter $\\beta_0$ is also called \"bias\" and $\\beta_1$ \"weights\". The particular values of these quantities that maximizes the likelyhood function are what we need to find to make predictions."
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   "source": [
    "# Defining the sigmoid function\n",
    "\n",
    "import numpy as np # Importing a linear algebra package\n",
    "import matplotlib.pyplot as plt # To plot figures\n",
    "\n",
    "def sigmoid(beta_1, beta_0, x):\n",
    "    return 1/(1+np.exp(-(beta_1*x-beta_0)))"
   ]
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K84zC/DwK8sO/eUZhQTC9oGl6Xt6BNgV5Rp4ZeXlGngWPY2bkW3C71XnhffPzSJpu5OWBEbQxMwDMwMK/wbXkaRZOaZpmYbvU0w66nbTcd06zpHkHLzdZqumWYmLzKSnv16xV15J4Y1Ccj74RGJJ0e3A4TUREpFX1jQk2VVazbsd+NlVWs7Wqli1VNWytqmHL7hq27alh+966Fu/fraSAXl2K6NG5iO6dixjcszNdiwvoWlJA1+ICSksK6FJc8I5pncKQVVL4r8BVUpBHQb5ONCBHJs4QNgO42cweBSYDuzUeTEREmrg7m3fXsGzrHlZs3cPaHfsp37mfdTv2s7GymsZmx+16dymiX7cS+ncv4cQh3enXrYS+pSX06lJEz86Fwd8uRfToVKjgJGkhshBmZo8AZwN9zGwD8HWgEMDdfwHMBC4CVgL7geujqkVERNJbbUMjSzbvYX55JUu3VLFsyx5WbN3LntqGA216di5kaO8unDikBxefOJChvTszrFdnBvXsRN/SEooKFKwks0T57cgrDzHfgf8X1eOLiEj62rBrP2+s2cm88krml1eyeHMV9Y1Bz1bPzoWM7VfKJacMYmy/Uo7pX8rYvqV071wYc9Ui7SsjBuaLiEhm21ZVw+zVO3h15Q5mr97B+p37AehSlM8Jg3tww1kjOWlId04Y3IMB3UtSDrwWyTYKYSIi0u7cncWbq3h+8TaeX7KVhRt3A8GA+Mkje3P9mcOZMrI3Y/uVkp+nwCW5SSFMRETahbuzcONu/vzPTfzf25vZtLsGMzh5SA9uueAY3j2mjPEDuyl0iYQUwkRE5KiU79zPn/65kT/P28jqin0U5efx7rFlfP68sZwzri9lpcVxlyiSlhTCRETksDUmnJeWbWP6a+t4eXkF7jBlZC9ufNdIph43QIPoRdpAIUxERNpsT009D72+numz17Gxspq+pcX823vHcNlpQxjUo1Pc5YlkFIUwERE5pJ376rjvlTU88OpaqmoamDKyF7e9/1jeN74fhTrxqcgRUQgTEZEWVe6v456XVvHg7HXUNDRy4YT+3HT2aI4f3D3u0kQynkKYiIgcpKa+kftfXcvPX1zJntoGLjlpEDedM4rRfUvjLk0kayiEiYjIAe7O0ws3852nl7Bpdw3nHFPGV6aOY1z/bnGXJpJ1FMJERASAtdv38V9/eZu/r9jO+AHd+OFlJ3H6qN5xlyWStRTCRERyXH1jgl+8tIqfvLiSovw8vv7B8VwzZRgFGnAvEimFMBGRHLZy216++Pg85m/YzftPGMDtHxhPv24lcZclkhMUwkREcpC788Cra/nuM0vpVJTPz686hYuOHxB3WSI5RSFMRCTH7K6u54uPz+f5JVs5+5gyvv+RE+ir3i+RDqcQJiKSQxZt2s1ND73Fxl3V3P6B8Vx/5nDM9IPaInFQCBMRyRF/+ucGbv3DQnp0LuSxT0/h1GG94i5JJKcphImIZDl353+fX8Hdf1vB5BG9+NlVp9Cna3HcZYnkPIUwEZEsVtvQyJefWMBf5m3i0lMH8+1LjqeoQKeeEEkHCmEiIlmqqqaeTz4wlzfW7OSWC47hprNHafyXSBpRCBMRyUI799Vx3W/fYMnmKn58xUlMO2lQ3CWJSDMKYSIiWWZbVQ1X/+Z11u7Yz73Xnsp7x/WLuyQRSUEhTEQki2zZXcMV985m255a7v/4aZwxuk/cJYlICxTCRESyxPa9tVz169fYvreO6TdM0ikoRNKcviIjIpIFdu+v55rfvMHGymp+c91EBTCRDKAQJiKS4fbWNvDx+99g1ba9/PKaiUwe2TvukkSkDXQ4UkQkg9U3JrjpobdYsGE3P7/qFN4ztizukkSkjdQTJiKSodyd2/+yiFnLK/j2h47jggn94y5JRA6DQpiISIb65azVPPLGem46exRXTBoadzkicpgUwkREMtDTCzbz388s5QMnDOBL5x8TdzkicgQUwkREMsySzVV88ffzOHVYT/7n0hPJy9NPEYlkIoUwEZEMUrm/jk9Pf5PunQq55+pTKCnMj7skETlC+nakiEiGaEw4//7oPDbvrubRG0+nb2lJ3CWJyFFQT5iISIa46/nlvLy8gq9/cAKnDusZdzkicpQUwkREMsDfV1TwkxdWcumpg7lqsr4JKZINFMJERNLc9r21fOHx+Yzu25U7px2HmQbii2QDjQkTEUlj7s4tv5/P7up6HvzEJDoVaSC+SLZQT5iISBq775W1vLisgtsuOpZjB3SLuxwRaUcKYSIiaWrJ5ir++5mlnHdsX649fVjc5YhIO1MIExFJQ/WNCb70+/l061TA9z5ygsaBiWShSEOYmV1oZsvMbKWZ3Zpi/lAze9HM/mlmC8zsoijrERHJFPe8tIpFm6r41oeOo3fX4rjLEZEIRBbCzCwf+BkwFRgPXGlm45s1+xrwuLufDFwB/DyqekREMsWSzVX85IUVfPDEgVx43IC4yxGRiETZEzYJWOnuq929DngUmNasjQNNI027A5sirEdEJO01HYbs3qmQb1w8Ie5yRCRCUZ6iYhBQnnR7AzC5WZs7gOfM7HNAF+C8COsREUl7vwgPQ/7i6lPo1aUo7nJEJEJxD8y/Erjf3QcDFwHTzeygmszsRjOba2ZzKyoqOrxIEZGOsHb7Pn7y4kouOr6/DkOK5IAoQ9hGYEjS7cHhtGQ3AI8DuPtsoATo03xB7n6vu09094llZWURlSsiEh935/YZiyjKz+P2D+gwpEguiDKEzQHGmNkIMysiGHg/o1mb9cC5AGZ2LEEIU1eXiOScmQu3MGt5BV9431j6dy+JuxwR6QCRhTB3bwBuBp4FlhB8C3KRmd1pZheHzb4IfMrM5gOPAB93d4+qJhGRdLSnpp47n1rEhIHddFJWkRwS6W9HuvtMYGazabcnXV8MnBllDSIi6e5Hf13Otj21/PKaiRTkxz1UV0Q6ivZ2EZEYLduyhwdeXcvHJg3lpCE94i5HRDqQQpiISEzcnW8+tZjSkkJuueCYuMsRkQ6mECYiEpMXlm7jHyu38x/njaFHZ50TTCTXKISJiMSgriHBt59ewqiyLlw1RYPxRXKRQpiISAymv7aO1dv38bX3j6dQg/FFcpL2fBGRDrZzXx0/fn457x5bxtnH6ATUIrlKIUxEpIPd/bcV7Ktr5GvvPxYzi7scEYmJQpiISAcq37mfh15fx2UThzC2X2nc5YhIjBTCREQ60P/+dTl5Znz+vDFxlyIiMVMIExHpIEu3VPGneRu5/swR9Oum34cUyXUKYSIiHeR/nl1G1+ICPvueUXGXIiJpQCFMRKQDzF27k+eXbOMz7xlF986FcZcjImlAIUxEJGLuzvf+byllpcVcf+bwuMsRkTShECYiErGXl1cwZ+0u/u3cMXQuKoi7HBFJEwphIiIRcnfuen4Fg3p04vKJQ+IuR0TSiEKYiEiEZq3YzrzySm46ZxRFBXrLFZF/0TuCiEhE3J0fP7+cgd1LuPRU9YKJyDsphImIROQfK7fz1vpKPnvOaPWCichB9K4gIhKBoBdsBQO6l3DZxMFxlyMiaUghTEQkArNX7WDuul189uxRFBfkx12OiKQhhTARkQjc9bcV9OtWzGX6RqSItEAhTESknb2+egdvrNnJZ98zipJC9YKJSGoKYSIi7eyel1fRu0sRV0waGncpIpLGFMJERNrR4k1VvLSsgk+cNUK9YCLSKoUwEZF29MtZq+hSlM/Vk4fFXYqIpDmFMBGRdlK+cz9Pzt/ExyYPpXvnwrjLEZE0pxAmItJOfvX31eTnGTecNTLuUkQkAyiEiYi0g+17a3lsTjmXnDyI/t1L4i5HRDKAQpiISDt44NW11DUmuPHdo+IuRUQyhEKYiMhR2lfbwIOz13H++H6M7ts17nJEJEMohImIHKVH3ljP7up6PvMe9YKJSNsphImIHIWGxgT3vbKWSSN6cfLQnnGXIyIZRCFMROQoPLtoKxsrq7nhrBFxlyIiGUYhTETkKPzmH6sZ2qsz5x3bL+5SRCTDKISJiByhf67fxVvrK7n+zOHk51nc5YhIhlEIExE5Qr/5xxpKiwu4dOKQuEsRkQykECYicgQ2VlbzzNtbuGLSELoWF8RdjohkIIUwEZEj8ODstbg7150xPO5SRCRDKYSJiBymfbUNPPL6eqYeN4DBPTvHXY6IZCiFMBGRw/SHtzZQVdPAJ3RaChE5CpGGMDO70MyWmdlKM7u1hTaXmdliM1tkZg9HWY+IyNFKJJz7XlnLSUN6cOownZxVRI5cZKNJzSwf+BnwPmADMMfMZrj74qQ2Y4CvAme6+y4z6xtVPSIi7eGFpdtYs30fP7ny5LhLEZEMF2VP2CRgpbuvdvc64FFgWrM2nwJ+5u67ANx9W4T1iIgctfteXcOA7iVMPa5/3KWISIaLMoQNAsqTbm8IpyUbC4w1s1fM7DUzuzDCekREjsrKbXt5ZeUOrp4yjIJ8DakVkaMT98ltCoAxwNnAYGCWmR3v7pXJjczsRuBGgKFDh3ZwiSIigYdeX0dhvnGZTs4qIu0gyn/lNgLJ71SDw2nJNgAz3L3e3dcAywlC2Tu4+73uPtHdJ5aVlUVWsIhIS/bXNfDEmxu46PgBlJUWx12OiGSBKEPYHGCMmY0wsyLgCmBGszZ/JugFw8z6EByeXB1hTSIiR+Qv8zaxp6aBa6YMi7sUEckSkYUwd28AbgaeBZYAj7v7IjO708wuDps9C+wws8XAi8At7r4jqppERI6Eu/Pg7HWM61+q01KISLuJdEyYu88EZjabdnvSdQe+EF5ERNLSW+t3sWRzFd+55HjMLO5yRCRL6Os9IiKHMH32OkqLC5h20sC4SxGRLKIQJiLSiu17a5m5cAsfOXUwXYrj/kK5iGQThTARkVY8NqecusYEV2tAvoi0M4UwEZEWNCach19fzxmjejO6b9e4yxGRLKMQJiLSgheWbmNjZTXXnq5eMBFpfwphIiItmP7aOvp1K+a8Y/vFXYqIZCGFMBGRFNZs38es5RV8bJJ+J1JEoqF3FhGRFB56bR0FecaVk/Q7kSISDYUwEZFmqusaeXxuORcc15++3UriLkdEspRCmIhIM0/O30RVTQPX6rQUIhIhhTARkSTuzoOvrWVsv65MGtEr7nJEJIsphImIJJlXXsnbG6u4Zsow/U6kiETqsEKYmXUxs/yoihERidv019bRpSifS04ZHHcpIpLlWg1hZpZnZh8zs6fNbBuwFNhsZovN7AdmNrpjyhQRid7OfXU8tWAzHz5lMF31O5EiErFD9YS9CIwCvgr0d/ch7t4XOAt4DfiemV0dcY0iIh3i8bnl1DUkuEZnyBeRDnCof/XOc/f65hPdfSfwB+APZlYYSWUiIh2oMeE89Po6Jo/oxdh+pXGXIyI5oNWesKYAZmbnNZ9nZtcltxERyWQvL99G+c5q9YKJSIdp68D8283snnBgfj8zexL4YJSFiYh0pOmz11FWWswFE/rHXYqI5Ii2hrD3AKuAecA/gIfd/aNRFSUi0pHW79jPS8sruHLSUAr1O5Ei0kHa+m7TE5hEEMRqgWGmE+iISJZ46PV15JnxsUlD4y5FRHJIW0PYa8D/ufuFwGnAQOCVyKoSEekgNfWNPDa3nPPH96N/d/1OpIh0nLaeCOc8d18P4O7VwL+Z2bujK0tEpGM8tWAzlfvruUa/EykiHexQJ2sdDtAUwJK5+ywL6LTSIpKxpr+2jlFlXTh9VO+4SxGRHHOonrAfmFke8BfgTaACKAFGA+cA5wJfBzZEWaSISBQWbKhkfnkld3xwvH4nUkQ6XKshzN0vNbPxwFXAJ4D+QDWwBJgJfNvdayKvUkQkAtNnr6NzUT4fPlUd+iLS8Q45MN/dFwPfAp4kCF9rgDnAEwpgIpKpKvfXMWP+Jj508iC6leiHP0Sk47V1YP4DQBVwd3j7Y8CDwGVRFCUiErXfz91AbUNCA/JFJDZtDWHHufv4pNsvmtniKAoSEYlaIuH87vV1nDa8J8cO6BZ3OSKSo9p6nrC3zGxK0w0zmwzMjaYkEZFozVpRwbod+7lavWAiEqO29oSdCrxqZk2nqhgKLDOzhYC7+wmRVCciEoHps9fRp2sxU48bEHcpIpLD2hrCLoy0ChGRDlK+cz8vLNvGzeeMpqhAvxMpIvFpUwhz93VRFyIi0hF+1/Q7kZP1O5EiEi/9GygiOaOmvpHH55TzvmP7MaB7p7jLEZEcpxAmIjnjqQWb2bW/nmtP14B8EYmfQpiI5Izps9cyum9X/U6kiKQFhTARyQnzyyuZv2E310wZpt+JFJG0oBAmIjnhwfB3Ii85ZVDcpYiIAAphIpIDdu6r48kFm7hEvxMpImlEIUxEst7jc8upa0hw7enD4y5FROQAhTARyWqNCed3r61j0oheHNO/NO5yREQOUAgTkaz20rJtbNhVrdNSiEjaiTSEmdmFZrbMzFaa2a2ttPuImbmZTYyyHhHJPQ/OXkff0mIumNA/7lJERN4hshBmZvnAz4CpwHjgSjMbn6JdKfDvwOtR1SIiuWnt9n28vLyCKycNpTBfHf8ikl6ifFeaBKx099XuXgc8CkxL0e6bwPeAmghrEZEc9MDstRTk6XciRSQ9RRnCBgHlSbc3hNMOMLNTgCHu/nSEdYhIDtpTU8/v527g/ScMoF+3krjLERE5SGz982aWB/wI+GIb2t5oZnPNbG5FRUX0xYlIxnvizQ3srW3g+jNHxF2KiEhKUYawjcCQpNuDw2lNSoHjgJfMbC0wBZiRanC+u9/r7hPdfWJZWVmEJYtINkgknPtfXcvJQ3tw0pAecZcjIpJSlCFsDjDGzEaYWRFwBTCjaaa773b3Pu4+3N2HA68BF7v73AhrEpEc8MLSbazbsV+9YCKS1iILYe7eANwMPAssAR5390VmdqeZXRzV44qI3PfqGvp3K2HqcTothYikr4IoF+7uM4GZzabd3kLbs6OsRURyw7Ite3hl5Q5uueAYnZZCRNKa3qFEJKvc/+oaigvy+NgknZZCRNKbQpiIZI2d++r441sb+fApg+jZpSjuckREWqUQJiJZ45E31lPbkODjZ2hAvoikP4UwEckK9Y0Jps9ex5mje3NM/9K4yxEROSSFMBHJCjMXbmZLVQ3XqxdMRDKEQpiIZDx3595ZqxlV1oX3jusbdzkiIm2iECYiGe/VVTtYtKmKT71rJHl5Fnc5IiJtohAmIhnvl7NW06drMR86eVDcpYiItJlCmIhktCWbq5i1vILrzxxOSWF+3OWIiLSZQpiIZLRfzVpN56J8rp48LO5SREQOi0KYiGSsTZXVzJi/ictPG0L3zoVxlyMiclgUwkQkY933yhocuOEsnZZCRDKPQpiIZKSqmnoeeaOc9x8/gME9O8ddjojIYVMIE5GM9PDr69lb28CN7x4ZdykiIkdEIUxEMk5NfSO//vtq3jWmD8cN6h53OSIiR0QhTEQyzqNvrGf73jo+994xcZciInLEFMJEJKPUNjTyy1mrmTSiF5NG9Iq7HBGRI6YQJiIZ5Y9vbWTz7ho+997RcZciInJUFMJEJGM0NCa456VVnDikB2eN7hN3OSIiR0UhTEQyxpMLNrF+535uPmc0ZvqhbhHJbAphIpIREgnnpy+sZFz/Us4d1zfuckREjppCmIhkhGfe3sKqin3c/N7R5OWpF0xEMp9CmIikvcaEc9fzyxndtytTjxsQdzkiIu1CIUxE0t6T8zexYttevvC+seSrF0xEsoRCmIiktfrGBHc9v5xjB3Tjwgn94y5HRKTdKISJSFr741sbWLtjP19831iNBRORrKIQJiJpq7ahkbv/tpITh/Tg3GP1jUgRyS4KYSKSth6bU87Gymq+dP5YnRdMRLKOQpiIpKXqukZ++sJKJo3opbPji0hWUggTkbT021fWsG1PLV86/xj1golIVlIIE5G0s31vLfe8tIr3je/HpBG94i5HRCQSCmEiknZ+/PwKqusbuXXquLhLERGJjEKYiKSVVRV7efiN9Vw5aQijyrrGXY6ISGQUwkQkrXzvmaWUFOTx7+eOjbsUEZFIKYSJSNp4Y81Onlu8lc+ePYqy0uK4yxERiZRCmIikhcaE882nFtO/Wwk3nDUy7nJERCKnECYiaeGxOeUs3Libr140jk5F+XGXIyISOYUwEYld5f46fvDsUiYN78XFJw6MuxwRkQ6hECYisfvhc8vZXV3PN6ZN0IlZRSRnKISJSKze3ribh15fx7WnD+fYAd3iLkdEpMNEGsLM7EIzW2ZmK83s1hTzv2Bmi81sgZn9zcyGRVmPiKSXRMK5Y8YienYu4j/ep1NSiEhuiSyEmVk+8DNgKjAeuNLMxjdr9k9gorufADwBfD+qekQk/Tw+t5y563bxlQvH0b1TYdzliIh0qCh7wiYBK919tbvXAY8C05IbuPuL7r4/vPkaMDjCekQkjWyrquHbM5cwZWQvLp2oXV9Eck+UIWwQUJ50e0M4rSU3AM9EWI+IpJGvz1hEbUOC7374BA3GF5GcVBB3AQBmdjUwEXhPC/NvBG4EGDp0aAdWJiJReHbRFp55ewu3XHAMI/p0ibscEZFYRNkTthEYknR7cDjtHczsPOA24GJ3r021IHe/190nuvvEsrKySIoVkY5RVVPP7X95m3H9S7nx3TozvojkrihD2BxgjJmNMLMi4ApgRnIDMzsZ+CVBANsWYS0ikia++eRiKvbU8r2PnEBhvs6SIyK5K7J3QHdvAG4GngWWAI+7+yIzu9PMLg6b/QDoCvzezOaZ2YwWFiciWeDZRVv4/Zsb+OzZozhxSI+4yxERiVWkY8LcfSYws9m025Ounxfl44tI+qjYU8tX/7iQCQO78e/n6pxgIiI6FiAikXN3vvrHBeytbeCuy0+iqEBvPSIieicUkcg9Oqec55ds4ysXjmNMv9K4yxERSQsKYSISqaVbqrhjxiLOHN2b688YHnc5IiJpQyFMRCKzt7aBmx56i26dCrnr8pPJy9NJWUVEmiiEiUgk3J3b/rSQtdv3cfcVJ1NWWhx3SSIiaUUhTEQi8cgb5fxl3ib+47yxnD6qd9zliIikHYUwEWl3b67bxR0zFvGuMX246ZzRcZcjIpKWFMJEpF1t3l3Np6e/yYAeJdx9xcnkaxyYiEhKafED3iKSHarrGvnUg3OpqW/k4U9NpmeXorhLEhFJWwphItIuEgnnlifms2hTFb++diJjdT4wEZFW6XCkiLSL7/3fUp5asJkvXzCOc4/tF3c5IiJpTyFMRI7ar/++ml/OWs01U4bxmfeMjLscEZGMoBAmIkflL/M28q2nlzD1uP7ccfEEzDQQX0SkLRTCROSIvbh0G1/6/Xwmj+jF/15+kr4JKSJyGBTCROSIvLRsG5+e/ibj+nfj3msnUlKYH3dJIiIZRSFMRA7by8sruHH6m4zp15XpN0yie6fCuEsSEck4OkWFiByWph6wUWVd+d0Nk+nRWecCExE5EuoJE5E2+8u8jXzygbmMKuvKQ5/UyVhFRI6GesJEpE3ue2UN33hyMZNH9OJX102kW4kOQYqIHA2FMBFpVSLh/OC5Zdzz0irOH9+Pu688WYPwRUTagUKYiLRob20D//HYPP66eCsfmzyUOy+eQEG+RjGIiLQHhTARSal8534++cBcVlbs5Y4Pjue6M4brRKwiIu1IIUxEDvLC0q188fH5NCac+68/jXeNKYu7JBGRrKMQJiIH1DUk+MGzS/nV39dw7IBu/PyqUxjRp0vcZYmIZCWFMBEBYM32fXz+sXnML6/kminDuO39x2oAvohIhBTCRHJcY8K575U1/M9zyyjKz+Oeq05h6vED4i5LRCTrKYSJ5LCV2/by5Sfm89b6Ss47ti/fvuR4+nUribssEZGcoBAmkoP21NTz0xdW8ttX1tCluIC7Lj+JaScN1LcfRUQ6kEKYSA5JJJw/z9vId59ZSsWeWi6bOJhbLhhHWWlx3KWJiOQchTCRHODuvLB0Gz98bjmLN1dx4pAe/OraiZw0pEfcpYmI5CyFMJEs5u68snIHP/zrMv65vpJhvTvzv5efyLQTB5GXp0OPIiJxUggTyUL1jQlmLtzMr/6+mrc3VjGgewnf/fDxfPTUwRTqZ4dERNKCQphIFtm5r44/vLmB+19dy8bKakaVdeG7Hz6eS04epHN+iYikGYUwkQyXSDivrNrOo3PKeW7RFuobnUkjenHntAmcc0xfHXYUEUlTCmEiGcjdeXtjFU8v3MxTCzaxYVc1PToXcvWUYVxx2lCO6V8ad4kiInIICmEiGaIx4czfUMlzi7Yyc+Fm1u/cT0GeccboPnz5wnGcP76fDjmKiGQQhTCRNLZtTw2zlm/n5eUV/H1FBZX768nPM84c3YebzxnN+RP60aNzUdxliojIEVAIE0kT7k75zmreWLuTuWt3MmftTlZV7AOgT9dizh3Xj7OPKeNdY/ooeImIZAGFMJEYuDubdtewaONuFm2qYtGm3SzYsJtte2oB6FZSwMThvfjoqUN415g+jB/QTQPsRUSyjEKYSIQSCWfT7mpWV+xjdcVeVm/fx6qKvSzeVMWu/fUAmMGosq6cMao3pw7vxWnDezK2b6lCl4hIllMIEzkKiYSzfV8tmypr2Lirmk2V1WwMLxt2VbNm+15q6hMH2peWFDCyrCsXTOjPhIHdGD+wO8cOKKVzkXZFEZFcE+k7v5ldCPwYyAd+7e7/3Wx+MfAgcCqwA7jc3ddGWZNIaxIJZ19dA1U1DVRV17NrXx0Ve2vZsbeO7Xtr2f6O63VU7KmlrjHxjmV0LS5gUI9ODOrZiTNH9WZkWVdGlnVhZFkXyroWY6YeLhERiTCEmVk+8DPgfcAGYI6ZzXD3xUnNbgB2uftoM7sC+B5weVQ1SXZwdxoSTn1jgvoGp64xQU19I9X1jVTXNbK/rvHA7f11TdMbqK5LHLi+t7aRPTX1VNXUU1XdEP6tZ29tAwlP/bgFeUbvrkX07lJMn9JiRvXtSllpcRC4enRiYHjp3qmwY58QERHJSFH2hE0CVrr7agAzexSYBiSHsGnAHeH1J4Cfmpm5ewsfg9HbVlXDvPJKmgr4VyV+4HbzeZ40718tg7DAodq2cB9Pmtjy8g+e/69yPXXbFNNT1ds0r9GdhDuJhJPw4FxViXBaY4ID8xrdg/YHrnvYlgPzD1xPWkbCCQJVQyIIVY0J6hr9wPX6huB2QyIRtvGDep4OR1F+HiWFeXQtLqBbp0K6lRQysEcJ40pK6dapkNKSArqVFNKtUwGlJYX07FxEWWkQvLp3KtQ4LRERaTdRhrBBQHnS7Q3A5JbauHuDme0GegPbkxuZ2Y3AjQBDhw6Nql4A/lleyaenvxnpY2Q6M8g3I8+MvDzIMwtu5xl5Bvl54Twz8vMsaJ8XtLEU8/PyjOL8PIoL8+haUkBhfh6F+Rb+DS5FTbcLmt0O25YU5tOpKJ/ORfnB9cJ8OhcV0Kkwn5KiPDqF0wr049UiIpImMmI0sLvfC9wLMHHixEh7yaaM7M1TnzsLCMIGgGHvvG0ppsE7bpNiftNYoOZtmy+LpPltvU/yw7ZcWyvLsubTAgcFpqSaRERE5MhFGcI2AkOSbg8Op6Vqs8HMCoDuBAP0Y9O9UyHdB3WPswQRERHJAVEem5kDjDGzEWZWBFwBzGjWZgZwXXj9o8ALcY4HExEREekokfWEhWO8bgaeJThFxW/dfZGZ3QnMdfcZwG+A6Wa2EthJENREREREsl6kY8LcfSYws9m025Ou1wCXRlmDiIiISDrSV8VEREREYqAQJiIiIhIDhTARERGRGCiEiYiIiMRAIUxEREQkBgphIiIiIjFQCBMRERGJgWXaCerNrAJYF/HD9KHZj4jnmFxe/1xed8jt9de6565cXv9cXnfomPUf5u5lqWZkXAjrCGY2190nxl1HXHJ5/XN53SG311/rnpvrDrm9/rm87hD/+utwpIiIiEgMFMJEREREYqAQltq9cRcQs1xe/1xed8jt9de6565cXv9cXneIef01JkxEREQkBuoJExEREYlBzoYwM7vUzBaZWcLMJjab91UzW2lmy8zsghbuP8LMXg/bPWZmRR1TefsL658XXtaa2bwW2q01s4Vhu7kdXGYkzOwOM9uYtP4XtdDuwvD1sNLMbu3oOqNiZj8ws6VmtsDM/mRmPVpolzXb/lDb0syKw31iZbiPD4+hzHZnZkPM7EUzWxy+9/17ijZnm9nupP3h9jhqjcqhXscWuDvc9gvM7JQ46mxvZnZM0jadZ2ZVZvb5Zm2yatub2W/NbJuZvZ00rZeZ/dXMVoR/e7Zw3+vCNivM7LpIC3X3nLwAxwLHAC8BE5OmjwfmA8XACGAVkJ/i/o8DV4TXfwF8Nu51aqfn5YfA7S3MWwv0ibvGdl7fO4AvHaJNfvg6GAkUha+P8XHX3k7rfz5QEF7/HvC9bN72bdmWwE3AL8LrVwCPxV13O637AOCU8HopsDzFup8NPBV3rRE+B62+joGLgGcAA6YAr8ddcwTPQT6wheDcVVm77YF3A6cAbydN+z5wa3j91lTvd0AvYHX4t2d4vWdUdeZsT5i7L3H3ZSlmTQMedfdad18DrAQmJTcwMwPeCzwRTnoA+FCE5XaIcL0uAx6Ju5Y0MwlY6e6r3b0OeJTgdZLx3P05d28Ib74GDI6zng7Qlm05jWCfhmAfPzfcNzKau29297fC63uAJcCgeKtKO9OABz3wGtDDzAbEXVQ7OxdY5e5Rn/Q8Vu4+C9jZbHLyvt3S5/YFwF/dfae77wL+ClwYVZ05G8JaMQgoT7q9gYPfqHoDlUkfXqnaZKJ3AVvdfUUL8x14zszeNLMbO7CuqN0cHnr4bQvd0215TWSDTxD0AqSSLdu+LdvyQJtwH99NsM9njfAQ68nA6ylmn25m883sGTOb0LGVRe5Qr+Nc2NevoOV/tLN52wP0c/fN4fUtQL8UbTr0NVAQ1YLTgZk9D/RPMes2d/9LR9cTpzY+F1fSei/YWe6+0cz6An81s6XhfxtprbV1B+4Bvknw5vxNgsOxn+i46qLXlm1vZrcBDcBDLSwmI7e9HMzMugJ/AD7v7lXNZr9FcJhqbzg+8s/AmA4uMUo5/ToOxy5fDHw1xexs3/bv4O5uZrGfHiKrQ5i7n3cEd9sIDEm6PTiclmwHQTd1Qfifcqo2aeVQz4WZFQAfBk5tZRkbw7/bzOxPBId20v4NrK2vAzP7FfBUillteU2krTZs+48DHwDO9XBQRIplZOS2T6Et27KpzYZwv+hOsM9nPDMrJAhgD7n7H5vPTw5l7j7TzH5uZn3cPSt+W7ANr+OM3tfbYCrwlrtvbT4j27d9aKuZDXD3zeFh5m0p2mwkGB/XZDDB2PFI6HDkwWYAV4TfkBpB8J/AG8kNwg+qF4GPhpOuAzK9Z+08YKm7b0g108y6mFlp03WCAd1vp2qbSZqN97iE1Os0BxhjwTdiiwi682d0RH1RM7MLgS8DF7v7/hbaZNO2b8u2nEGwT0Owj7/QUjjNJOG4tt8AS9z9Ry206d80/s3MJhF8RmRLAG3L63gGcG34LckpwO6kw1fZoMWjHdm87ZMk79stfW4/C5xvZj3D4Snnh9Oi0ZHfVkinC8EH7gagFtgKPJs07zaCb1AtA6YmTZ8JDAyvjyQIZyuB3wPFca/TUT4f9wOfaTZtIDAzaX3nh5dFBIeyYq+7HdZ7OrAQWECwgw5ovu7h7YsIvk22KlvWPVyvlQTjH+aFl6ZvBWbttk+1LYE7CYIoQEm4T68M9/GRcdfcTut9FsFh9wVJ2/si4DNN+z5wc7iN5xN8UeOMuOtux/VP+Tputv4G/Cx8bSwk6ZvzmX4BuhCEqu5J07J22xOEzc1AffhZfwPB2M6/ASuA54FeYduJwK+T7vuJcP9fCVwfZZ06Y76IiIhIDHQ4UkRERCQGCmEiIiIiMVAIExEREYmBQpiIiIhIDBTCRERERGKgECYiIiISA4UwERERkRgohIlIzjKz08Ifby8Jz6i+yMyOi7suEckNOlmriOQ0M/sWwVnyOwEb3P27MZckIjlCIUxEclr4G5JzgBqCn2ppjLkkEckROhwpIrmuN9AVKCXoERMR6RDqCRORnGZmM4BHgREEP+B+c8wliUiOKIi7ABGRuJjZtUC9uz9sZvnAq2b2Xnd/Ie7aRCT7qSdMREREJAYaEyYiIiISA4UwERERkRgohImIiIjEQCFMREREJAYKYSIiIiIxUAgTERERiYFCmIiIiEgMFMJEREREYvD/AZlS8KEvdqgGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10,10,10000) # Defining a interval\n",
    "y = sigmoid(1,0,x) # Defining the dependent variable\n",
    "plt.figure(figsize=(10,5))\n",
    "plt.plot(x, y)\n",
    "plt.title(\"Sigmoid: the probability distribution of logistic model\")\n",
    "plt.xlabel(xlabel=\"x\")\n",
    "plt.ylabel(ylabel=\"p(x)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09aa4fa6",
   "metadata": {
    "papermill": {
     "duration": 0.014951,
     "end_time": "2023-02-22T14:58:47.031207",
     "exception": false,
     "start_time": "2023-02-22T14:58:47.016256",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Types of Logistic Regression\n",
    "\n",
    "1. **Binary Logistic Regression:** In this case the categorical variable (target) has only two possible outcomes. Examples: Spam or Not, diagnostic positive or negative, some equipment failed or not, students pass or fail in an exam.\n",
    "\n",
    "2. **Multinomial Logistic Regression:** The target contains three or more categories without ordering. Examples: Predicting if a individual is vegetarian, meat-eater or vegan, customer segmentation.\n",
    "\n",
    "3. **Ordinal Logistic Regression:** The target containd three or more categories with ordering. Example: Movie rating from 1 to 5.\n",
    "\n",
    "In this tutorial we will implement from scratch a binary logistic regression model.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e28808f",
   "metadata": {
    "papermill": {
     "duration": 0.014649,
     "end_time": "2023-02-22T14:58:47.061341",
     "exception": false,
     "start_time": "2023-02-22T14:58:47.046692",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Example\n",
    "\n",
    "The binary logistic regression can be used with one **explanatory variable** and two **categories** to answer a question. As an example, consider the case of a group of students which are preparing for a exam. The question is: how does the number of study hours affect the probability of the student passing the exam? In this case the explanatory variable is the number of hours studying and the two categories are being approved or not. Let's consider 10 students that spends between 0 to 10 hours studing and use 1 to identify \"pass\" and 0 to \"fail\". Then, we have the following \"sintetic\" data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3e30fbd7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:47.093922Z",
     "iopub.status.busy": "2023-02-22T14:58:47.093067Z",
     "iopub.status.idle": "2023-02-22T14:58:47.117090Z",
     "shell.execute_reply": "2023-02-22T14:58:47.115856Z"
    },
    "papermill": {
     "duration": 0.043233,
     "end_time": "2023-02-22T14:58:47.119527",
     "exception": false,
     "start_time": "2023-02-22T14:58:47.076294",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Hours</th>\n",
       "      <th>Pass</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>4.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>6.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>10.0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Hours  Pass\n",
       "0    0.0     0\n",
       "1    1.0     0\n",
       "2    2.5     0\n",
       "3    4.0     0\n",
       "4    4.0     1\n",
       "5    4.5     0\n",
       "6    5.0     1\n",
       "7    6.0     1\n",
       "8    8.0     1\n",
       "9   10.0     1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd # Data set management\n",
    "\n",
    "df = pd.DataFrame(data={\"Hours\":[0,1,2.5,4,4,4.5,5,6,8,10],\"Pass\":[0,0,0,0,1,0,1,1,1,1]})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2f0a7e0",
   "metadata": {
    "papermill": {
     "duration": 0.014543,
     "end_time": "2023-02-22T14:58:47.148944",
     "exception": false,
     "start_time": "2023-02-22T14:58:47.134401",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "To predict if a student will pass or not we need to consider the loss function, which is a function that represents the \"price to pay\" for inaccuracy of predictions. Usually, the logistic loss function is used as the measure of goodness of a fit in logistic regression. Considering that $p_k$ is the probability that the $k-$th student will pass the exam and $1-p_k$ the fail probability, the log loss for the $k-$th point is:\n",
    "$$ \\begin{cases}\n",
    "-\\ln p_{k} & \\text{if }y_{k}=1\\\\\n",
    "-\\ln(1-p_{k}) & \\text{if }y_{k}=0\n",
    "\\end{cases} $$\n",
    "\n",
    "Note that log loss is always greater than or equal to 0, equals 0 only in case of a perfect prediction, and approaches to infinity when predictions get worse. The two cases can be combined into a function called cross entropy:\n",
    "$$ -y_k \\ln p_k -(1-y_k) \\ln (1-p_k) $$\n",
    "\n",
    "The sum of the this term for all elements is the negative likelihood function:\n",
    "$$ -l = -\\sum_k^N [y_k \\ln p_k +(1-y_k) \\ln (1-p_k)]$$\n",
    "\n",
    "To estimate the probability of an outcome we need to find the values of $\\beta_0$ and $\\beta_1$ that minimizes the negative likelihood (or maximizes the positive likelihood, if you prefer). This is accomplished taking the derivative of the likelihood with respect to these parameters (or applying the gradient operator in high dimension problems):\n",
    "$$ 0 = \\frac{\\partial l}{\\partial \\beta_0} = \\sum_{k=1}^N(y_k-p_k) $$\n",
    "$$ 0 = \\frac{\\partial l}{\\partial \\beta_1} = \\sum_{k=1}^N(y_k-p_k)x_k $$\n",
    "Then we need to solve the above two equations for  $\\beta_{0}$ and $\\beta_{1}$, which generally requires the use of numerical methods. For example, we may start with $\\beta_0 = 0$ and $ \\beta_1 = 0$ and iterate the model increasing these parameters by a fraction of the gradient. After that, the probability of passing or failing the exam can be calculated using the sigmoid function\n",
    "$$ p = \\dfrac{1}{1+e^{-t}}\\,,$$\n",
    "where $t = \\beta_0 + x\\beta_1$. Let's implement this calculation using python functions\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c54c8c1",
   "metadata": {
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     "start_time": "2023-02-22T14:58:47.164471",
     "status": "completed"
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    "tags": []
   },
   "source": [
    "# Our Implementation\n",
    "\n",
    " We will start with $\\beta_0 = 0$ and $ \\beta_1 = 0.01(1,1,\\dots,1)$ and iterate the model increasing these parameters by a fraction of the gradient. This fraction amount is usually called \"learning rate\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ca99c8e7",
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "# Defining the initial parameters (zeros)\n",
    "def weightInitialization(n_features):\n",
    "    beta_1 = np.full((n_features),0) # Note that beta_1 must have the same dimension of x\n",
    "    beta_0 = 0\n",
    "    return beta_1,beta_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f0379f0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:47.280118Z",
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   "outputs": [],
   "source": [
    "# Defining the sigmoid function\n",
    "def sigmoid_vec(t):\n",
    "    p = 1/(1+np.exp(-t)) \n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "adf4cee2",
   "metadata": {
    "execution": {
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   "outputs": [],
   "source": [
    "# Calculates the likelihood and the derivatives\n",
    "def log_model(beta_1, beta_0, x, y):\n",
    "       \n",
    "    #Prediction\n",
    "    t = np.dot(beta_1, x.T) + beta_0 # The .T means the transpose of x and np.dot the dot product\n",
    "    prob = sigmoid_vec(t)\n",
    "    y = np.array(y)\n",
    "    likelihood = np.sum( -y*np.log(prob) - (1 - y)*np.log(1 - prob) )/x.shape[1] # The factor 1/x.shape[1] is for scaling by the n# of features\n",
    "    \n",
    "    #Gradient calculation\n",
    "    dbeta_1 = np.dot(x.T, (prob-y))/x.shape[1]\n",
    "    dbeta_0 = np.sum(prob-y)/x.shape[1]\n",
    "    \n",
    "    gradients = {\"dbeta_1\": dbeta_1, \"dbeta_0\": dbeta_0}\n",
    "    \n",
    "    return gradients, likelihood, prob "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "931d9fa7",
   "metadata": {
    "execution": {
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     "status": "completed"
    },
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   "outputs": [],
   "source": [
    "# Iterate the model to make it learn\n",
    "def model_predict(n_features, x, y, learning_rate, n_iterations):\n",
    "    beta_1, beta_0 = weightInitialization(n_features)\n",
    "    costs = []\n",
    "    \n",
    "    for i in range(n_iterations):\n",
    "        \n",
    "        gradients, likelihood, prob = log_model(beta_1, beta_0, x, y)\n",
    "        \n",
    "        dbeta_1 = gradients[\"dbeta_1\"]\n",
    "        dbeta_0 = gradients[\"dbeta_0\"]\n",
    "        #weight update\n",
    "        beta_1 = beta_1 - (learning_rate * dbeta_1)\n",
    "        beta_0 = beta_0 - (learning_rate * dbeta_0)\n",
    "        costs.append(likelihood)\n",
    "        \n",
    "            \n",
    "    #final parameters\n",
    "    y_prob = prob\n",
    "    parameters = {\"beta_1\": beta_1, \"beta_0\": beta_0}\n",
    "    gradient = {\"dbeta_1\": dbeta_1, \"dbeta_0\": dbeta_0}\n",
    "        \n",
    "    return parameters, gradient, costs, y_prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "187f627b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:47.407430Z",
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     "shell.execute_reply": "2023-02-22T14:58:47.412592Z"
    },
    "papermill": {
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     "end_time": "2023-02-22T14:58:47.416240",
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   "outputs": [],
   "source": [
    "# Create an array with the final predictions\n",
    "# Given a bias beta_0, a weight beta_1 and a input x return the predicted probability of pass or fail\n",
    "def predict(beta_1, beta_0, x): \n",
    "    t = np.dot(beta_1, x.T) + beta_0\n",
    "    z = sigmoid_vec(t)\n",
    "    y_pred = np.zeros(x.shape[0])\n",
    "    for i in range(y_pred.shape[0]):\n",
    "        if z[i] > 0.5:\n",
    "            y_pred[i] = 1\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34d0b5e7",
   "metadata": {
    "papermill": {
     "duration": 0.014725,
     "end_time": "2023-02-22T14:58:47.445927",
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Finally, we define a function to encompass all the functions above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7feb571",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:47.478496Z",
     "iopub.status.busy": "2023-02-22T14:58:47.478072Z",
     "iopub.status.idle": "2023-02-22T14:58:47.484923Z",
     "shell.execute_reply": "2023-02-22T14:58:47.483602Z"
    },
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     "duration": 0.026336,
     "end_time": "2023-02-22T14:58:47.487419",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Defining our logistic regression model\n",
    "def my_Logistic_Regression(x_train, y_train, x_test, learning_rate, n_iterations):\n",
    "    n_features = x_train.shape[1] # Dimension of the input\n",
    "    beta_1, beta_0 = weightInitialization(n_features) # Defined above\n",
    "    parameters, gradients, costs, y_prob = model_predict(n_features, x_train, y_train, learning_rate, n_iterations)# Defined above\n",
    "    y_pred = predict(parameters[\"beta_1\"], parameters[\"beta_0\"], x_test) # Defined above\n",
    "    return y_pred, y_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9baad800",
   "metadata": {
    "papermill": {
     "duration": 0.014645,
     "end_time": "2023-02-22T14:58:47.517410",
     "exception": false,
     "start_time": "2023-02-22T14:58:47.502765",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Now, we will load the Scikit Learning implementation of Logistic Regression to compare with our implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be7e2569",
   "metadata": {
    "papermill": {
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Scikit Learning Implementation\n",
    "\n",
    "The Scikit Learn `linear_model.LogisticRegression()` class implements a regularized logistic regression. his implementation can fit binary, One-vs-Rest, or multinomial logistic regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c98ed9c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:47.579787Z",
     "iopub.status.busy": "2023-02-22T14:58:47.579376Z",
     "iopub.status.idle": "2023-02-22T14:58:48.867036Z",
     "shell.execute_reply": "2023-02-22T14:58:48.865778Z"
    },
    "papermill": {
     "duration": 1.307033,
     "end_time": "2023-02-22T14:58:48.869942",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "077c0f04",
   "metadata": {
    "papermill": {
     "duration": 0.014734,
     "end_time": "2023-02-22T14:58:48.900371",
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     "start_time": "2023-02-22T14:58:48.885637",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Let's us import a data set to make predictions. As an example we will use a data set from National Institute of Diabetes and Digestive and Kidney Diseases. The objective of the dataset is to diagnostically predict whether a patient has diabetes, based on certain diagnostic measurements included in the dataset. Several constraints were placed on the selection of  these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "abd62199",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:48.932309Z",
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     "shell.execute_reply": "2023-02-22T14:58:48.960105Z"
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Pregnancies</th>\n",
       "      <th>Glucose</th>\n",
       "      <th>BloodPressure</th>\n",
       "      <th>SkinThickness</th>\n",
       "      <th>Insulin</th>\n",
       "      <th>BMI</th>\n",
       "      <th>DiabetesPedigreeFunction</th>\n",
       "      <th>Age</th>\n",
       "      <th>Outcome</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "   Pregnancies  Glucose  BloodPressure  SkinThickness  Insulin   BMI  \\\n",
       "0            6      148             72             35        0  33.6   \n",
       "1            1       85             66             29        0  26.6   \n",
       "2            8      183             64              0        0  23.3   \n",
       "3            1       89             66             23       94  28.1   \n",
       "4            0      137             40             35      168  43.1   \n",
       "\n",
       "   DiabetesPedigreeFunction  Age  Outcome  \n",
       "0                     0.627   50        1  \n",
       "1                     0.351   31        0  \n",
       "2                     0.672   32        1  \n",
       "3                     0.167   21        0  \n",
       "4                     2.288   33        1  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "diabetes_df = pd.read_csv('/kaggle/input/diabetes-dataset/diabetes.csv')\n",
    "diabetes_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35f4b863",
   "metadata": {
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     "duration": 0.015014,
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     "status": "completed"
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    "tags": []
   },
   "source": [
    "The outcome collumn dysplay 1 for a positive diabetes diagnostic and 0 for negative. \n",
    "\n",
    "Now, we will remove this columns and split the data in a train and test data frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e07550eb",
   "metadata": {
    "execution": {
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 768 entries, 0 to 767\n",
      "Data columns (total 9 columns):\n",
      " #   Column                    Non-Null Count  Dtype  \n",
      "---  ------                    --------------  -----  \n",
      " 0   Pregnancies               768 non-null    int64  \n",
      " 1   Glucose                   768 non-null    int64  \n",
      " 2   BloodPressure             768 non-null    int64  \n",
      " 3   SkinThickness             768 non-null    int64  \n",
      " 4   Insulin                   768 non-null    int64  \n",
      " 5   BMI                       768 non-null    float64\n",
      " 6   DiabetesPedigreeFunction  768 non-null    float64\n",
      " 7   Age                       768 non-null    int64  \n",
      " 8   Outcome                   768 non-null    int64  \n",
      "dtypes: float64(2), int64(7)\n",
      "memory usage: 54.1 KB\n"
     ]
    }
   ],
   "source": [
    "diabetes_df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4026fa58",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.091975Z",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "y = diabetes_df['Outcome']\n",
    "X = diabetes_df.drop(axis=1, columns='Outcome')\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1, test_size=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04b56ccb",
   "metadata": {
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     "duration": 0.015564,
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     "start_time": "2023-02-22T14:58:49.120597",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Fit the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "bc6b19df",
   "metadata": {
    "execution": {
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     "status": "completed"
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    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(max_iter=150, random_state=1)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Defining our logistic regression model fixing a random state (to do always the same predictions) and the number of iterations \n",
    "sk_model = LogisticRegression(random_state=1, max_iter=150)\n",
    "# Training our model\n",
    "sk_model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f98c2de8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.257957Z",
     "iopub.status.busy": "2023-02-22T14:58:49.257063Z",
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     "shell.execute_reply": "2023-02-22T14:58:49.263729Z"
    },
    "papermill": {
     "duration": 0.02824,
     "end_time": "2023-02-22T14:58:49.267404",
     "exception": false,
     "start_time": "2023-02-22T14:58:49.239164",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Making predictions\n",
    "sk_predictions = sk_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dff9747e",
   "metadata": {
    "papermill": {
     "duration": 0.015231,
     "end_time": "2023-02-22T14:58:49.298075",
     "exception": false,
     "start_time": "2023-02-22T14:58:49.282844",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Measuring performance of Scikit Learning predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a6fd764-fabd-4d68-b25e-dd53918dcdd2",
   "metadata": {
    "papermill": {
     "duration": 0.017585,
     "end_time": "2023-02-22T14:58:52.850263",
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     "start_time": "2023-02-22T14:58:52.832678",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Confusion Matrix\n",
    "\n",
    "The confusion matrix can tells us the number of true/false positive/negative predictions. By the time, we can calculate the precision rate, the missclassification rate, accuracy, prevalacence, etc. Let's see with more details the quantities that we can calculate using confusion matrix:\n",
    "\n",
    "1) Accuracy = (TP+TN/total) Is the overall evaluation of the classifier.\n",
    "\n",
    "2) Sensitivity = TP/(actual number of 1's) Indicates how many times 1 is predicted correctly.\n",
    "\n",
    "3) Fall-out = FP/(actual number of 0's) Indicates how many times 1 is predicted when actual answer is 0.\n",
    "\n",
    "4) Specificity = TN/(actual number of 0's) Indicates how many times 0 is predicted correctly.\n",
    "\n",
    "5) Misclassification Rate = (FP+FN)/(total) Tells about how often our model is wrong.\n",
    "\n",
    "6) Precision = TP/(TP + FP) Gives the rate of correct predictions.\n",
    "\n",
    "7) Prevalence = (actual number of 1's /total) Indicates how often condition 1 really occurs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a9feb0ac",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.332521Z",
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    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Importing a metric\n",
    "from sklearn.metrics import accuracy_score, classification_report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "27b2df50",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.373651Z",
     "iopub.status.busy": "2023-02-22T14:58:49.372797Z",
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     "shell.execute_reply": "2023-02-22T14:58:49.379866Z"
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7708333333333334"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sk_score = accuracy_score(y_test, sk_predictions)\n",
    "sk_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "18703b14",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.418874Z",
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     "shell.execute_reply": "2023-02-22T14:58:49.428116Z"
    },
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    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.78      0.89      0.83       246\n",
      "           1       0.74      0.57      0.64       138\n",
      "\n",
      "    accuracy                           0.77       384\n",
      "   macro avg       0.76      0.73      0.74       384\n",
      "weighted avg       0.77      0.77      0.76       384\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(y_test, sk_predictions))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a64fff1b",
   "metadata": {
    "papermill": {
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     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "This means that the Scikit Learning logistic model with the parameters choice above hit the predictions nearly $77\\%$ of the time, for the Diabets dataset. Its not so good having $23\\%$ of a population being incorrectly diagnosed, but its important to note that this is a simple example, to improve this score one can vary some parameters of the Logistic Regression class and fetch for correlation between the dependent variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d3a4068a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.501043Z",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Predict the classes on the test data, and return the probabilities for each class\n",
    "sk_y_prob = sk_model.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "73f0d2fc",
   "metadata": {
    "execution": {
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Calculate the Cumulative Distribution Finction (CDF)\n",
    "def cdf(sample, x, sort = False):\n",
    "    '''\n",
    "    Return the value of the Cumulative Distribution Function, evaluated for a given sample and a value x.\n",
    "    \n",
    "    Args:\n",
    "        sample: The list or array of observations.\n",
    "        x: The value for which the numerical cdf is evaluated.\n",
    "    \n",
    "    Returns:\n",
    "        cdf = CDF_{sample}(x)\n",
    "    '''\n",
    "    \n",
    "    # Sorts the sample, if needed\n",
    "    if sort:\n",
    "        sample.sort()\n",
    "    \n",
    "    # Counts how many observations are below x\n",
    "    cdf = sum(sample <= x)\n",
    "    \n",
    "    # Divides by the total number of observations\n",
    "    cdf = cdf / len(sample)\n",
    "    \n",
    "    return cdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "20eeae8d",
   "metadata": {
    "execution": {
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    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Gets the class CDFs\n",
    "def get_classes_cdf(y_real, y_proba):\n",
    "    # Unite both visions to be able to filter\n",
    "    df = pd.DataFrame()\n",
    "    df['real'] = y_real\n",
    "    df['proba'] = y_proba\n",
    "    \n",
    "    # Recover each class\n",
    "    class0 = df[df['real'] == 0].sort_values('proba')\n",
    "    class1 = df[df['real'] == 1].sort_values('proba')\n",
    "    \n",
    "    # Calculates the cdfs\n",
    "    cdf0 = np.array([cdf(class0['proba'].values, x, sort = False) for x in class0['proba'].values])\n",
    "    cdf1 = np.array([cdf(class1['proba'].values, x, sort = False) for x in class1['proba'].values])\n",
    "    \n",
    "    # Results\n",
    "    results =  {\n",
    "        'cdf0': cdf0,\n",
    "        'cdf1': cdf1,\n",
    "        'proba0': class0['proba'].values, \n",
    "        'proba1': class1['proba'].values, \n",
    "    }\n",
    "    \n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "00c74c2b",
   "metadata": {
    "execution": {
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    "tags": []
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   "outputs": [],
   "source": [
    "sk_cdf = get_classes_cdf(y_test, sk_y_prob[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d749185b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:49.849450Z",
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     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import seaborn as sns # Data visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "76838441",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.097324Z",
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   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the ROC curve\n",
    "fig = plt.figure(figsize = (10, 6))\n",
    "ax1 = plt.subplot()\n",
    "\n",
    "ax1.set_title(\"Scikit Learning Cumulative Distribution Function (CDF)\")\n",
    "sns.lineplot(x = sk_cdf['proba0'], y = sk_cdf['cdf0'], color = 'b', ax = ax1, linewidth = 3)\n",
    "sns.lineplot(x = sk_cdf['proba1'], y = sk_cdf['cdf1'], color = 'g', ax = ax1, linewidth = 3)\n",
    "ax1.legend([\"class 0\", \"class 1\"])\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "47fcc5c5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.554164Z",
     "iopub.status.busy": "2023-02-22T14:58:50.553711Z",
     "iopub.status.idle": "2023-02-22T14:58:50.559536Z",
     "shell.execute_reply": "2023-02-22T14:58:50.558200Z"
    },
    "papermill": {
     "duration": 0.0272,
     "end_time": "2023-02-22T14:58:50.562353",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.535153",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scipy.stats import ks_2samp # Kolmogorv-Smirnov (KS) Test\n",
    "from sklearn.metrics import roc_auc_score #ROC Area Under Curve (AUC) score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ea7f4e65",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.597460Z",
     "iopub.status.busy": "2023-02-22T14:58:50.596982Z",
     "iopub.status.idle": "2023-02-22T14:58:50.604526Z",
     "shell.execute_reply": "2023-02-22T14:58:50.603342Z"
    },
    "papermill": {
     "duration": 0.028067,
     "end_time": "2023-02-22T14:58:50.606790",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.578723",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Calculate the KS and the AUC values\n",
    "def evaluate_ks_and_roc_auc(y_real, y_proba):\n",
    "    # Unite both visions to be able to filter\n",
    "    df = pd.DataFrame()\n",
    "    df['real'] = y_real\n",
    "    df['proba'] = y_proba\n",
    "    \n",
    "    # Recover each class\n",
    "    class0 = df[df['real'] == 0]\n",
    "    class1 = df[df['real'] == 1]\n",
    "    \n",
    "    ks = ks_2samp(class0['proba'], class1['proba'])\n",
    "    roc_auc = roc_auc_score(df['real'] , df['proba'])\n",
    "    \n",
    "    print(f\"KS: {ks.statistic:.4f} (p-value: {ks.pvalue:.3e})\")\n",
    "    print(f\"ROC AUC: {roc_auc:.4f}\")\n",
    "    \n",
    "    return ks.statistic, roc_auc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7734132a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.643014Z",
     "iopub.status.busy": "2023-02-22T14:58:50.642165Z",
     "iopub.status.idle": "2023-02-22T14:58:50.657224Z",
     "shell.execute_reply": "2023-02-22T14:58:50.655492Z"
    },
    "papermill": {
     "duration": 0.03636,
     "end_time": "2023-02-22T14:58:50.659790",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.623430",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scikit Learning classifier:\n",
      "KS: 0.5274 (p-value: 2.401e-23)\n",
      "ROC AUC: 0.8303\n"
     ]
    }
   ],
   "source": [
    "print(\"Scikit Learning classifier:\")\n",
    "ks_sk, auc_sk = evaluate_ks_and_roc_auc(y_test, sk_y_prob[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "68837d23",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.695049Z",
     "iopub.status.busy": "2023-02-22T14:58:50.694175Z",
     "iopub.status.idle": "2023-02-22T14:58:50.699290Z",
     "shell.execute_reply": "2023-02-22T14:58:50.698367Z"
    },
    "papermill": {
     "duration": 0.025226,
     "end_time": "2023-02-22T14:58:50.701654",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.676428",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve # Build the Receiver Operating Characteristic Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "e4f21e0a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.738319Z",
     "iopub.status.busy": "2023-02-22T14:58:50.736991Z",
     "iopub.status.idle": "2023-02-22T14:58:50.748047Z",
     "shell.execute_reply": "2023-02-22T14:58:50.746368Z"
    },
    "papermill": {
     "duration": 0.032088,
     "end_time": "2023-02-22T14:58:50.750949",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.718861",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "logit_roc_auc = roc_auc_score(y_test, sk_predictions) \n",
    "fpr, tpr, thresholds = roc_curve(y_test, sk_y_prob[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "53444398",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:50.786955Z",
     "iopub.status.busy": "2023-02-22T14:58:50.785759Z",
     "iopub.status.idle": "2023-02-22T14:58:51.047212Z",
     "shell.execute_reply": "2023-02-22T14:58:51.045786Z"
    },
    "papermill": {
     "duration": 0.281945,
     "end_time": "2023-02-22T14:58:51.049747",
     "exception": false,
     "start_time": "2023-02-22T14:58:50.767802",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8)) \n",
    "plt.plot(fpr, tpr, label='Logistic Regression (area = %0.2f)' % logit_roc_auc) \n",
    "plt.plot([0, 1], [0, 1],'r--') \n",
    "plt.text(0.5, 0.5, \"varying threshold scores (0-1)\", rotation=0, size=12,ha=\"center\", va=\"center\",bbox=dict(boxstyle=\"rarrow\"))\n",
    "plt.xlabel('False Positive Rate') \n",
    "plt.ylabel('True Positive Rate') \n",
    "plt.title('Receiver operating characteristic') \n",
    "plt.legend(loc=\"lower right\") \n",
    "#plt.savefig('Log_ROC') \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13dd5048",
   "metadata": {
    "papermill": {
     "duration": 0.018011,
     "end_time": "2023-02-22T14:58:51.086594",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.068583",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Comparing our Logistic Model with the Scikit Learning Class "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "2bc7b3c4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:51.123703Z",
     "iopub.status.busy": "2023-02-22T14:58:51.123250Z",
     "iopub.status.idle": "2023-02-22T14:58:51.761733Z",
     "shell.execute_reply": "2023-02-22T14:58:51.760358Z"
    },
    "papermill": {
     "duration": 0.66082,
     "end_time": "2023-02-22T14:58:51.764621",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.103801",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "my_pred, y_prob = my_Logistic_Regression(X_train, y_train, X_test, learning_rate=1e-6, n_iterations=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "7cbb4092",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:51.800871Z",
     "iopub.status.busy": "2023-02-22T14:58:51.800326Z",
     "iopub.status.idle": "2023-02-22T14:58:51.809185Z",
     "shell.execute_reply": "2023-02-22T14:58:51.807914Z"
    },
    "papermill": {
     "duration": 0.029988,
     "end_time": "2023-02-22T14:58:51.811758",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.781770",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6432291666666666"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, my_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b80b1528",
   "metadata": {
    "papermill": {
     "duration": 0.017005,
     "end_time": "2023-02-22T14:58:51.845930",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.828925",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Our implementation scored relatively well compared to the Scikit Learning class for this particular case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41836a1f",
   "metadata": {
    "papermill": {
     "duration": 0.016758,
     "end_time": "2023-02-22T14:58:51.879663",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.862905",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Note:** The best result is reached when the learning rate is chosen to avoid the gradients being much greater (or smaller) than the parameters $\\beta$. For this particular dataset the learning rate of the order of $10^{-6}$ performs well.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "746aa56a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:51.915586Z",
     "iopub.status.busy": "2023-02-22T14:58:51.915175Z",
     "iopub.status.idle": "2023-02-22T14:58:52.540274Z",
     "shell.execute_reply": "2023-02-22T14:58:52.538836Z"
    },
    "papermill": {
     "duration": 0.646456,
     "end_time": "2023-02-22T14:58:52.543222",
     "exception": false,
     "start_time": "2023-02-22T14:58:51.896766",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "par, grad, costs, prob = model_predict(X_train.shape[1], X_train, y_train, 1e-6, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "28bfb0e9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:52.580185Z",
     "iopub.status.busy": "2023-02-22T14:58:52.579664Z",
     "iopub.status.idle": "2023-02-22T14:58:52.812101Z",
     "shell.execute_reply": "2023-02-22T14:58:52.810767Z"
    },
    "papermill": {
     "duration": 0.254125,
     "end_time": "2023-02-22T14:58:52.814921",
     "exception": false,
     "start_time": "2023-02-22T14:58:52.560796",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Likelihood')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (10, 6))\n",
    "plt.plot(costs)\n",
    "\n",
    "plt.xlabel(xlabel=\"Iterations\")\n",
    "plt.ylabel(ylabel=\"Likelihood\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "52d482ea",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:52.887487Z",
     "iopub.status.busy": "2023-02-22T14:58:52.887010Z",
     "iopub.status.idle": "2023-02-22T14:58:52.895582Z",
     "shell.execute_reply": "2023-02-22T14:58:52.894327Z"
    },
    "papermill": {
     "duration": 0.030366,
     "end_time": "2023-02-22T14:58:52.898207",
     "exception": false,
     "start_time": "2023-02-22T14:58:52.867841",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "c_matrix = confusion_matrix(y_test, my_pred) # Calculate the confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "518605d5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:52.934833Z",
     "iopub.status.busy": "2023-02-22T14:58:52.934419Z",
     "iopub.status.idle": "2023-02-22T14:58:53.205757Z",
     "shell.execute_reply": "2023-02-22T14:58:53.204626Z"
    },
    "papermill": {
     "duration": 0.292788,
     "end_time": "2023-02-22T14:58:53.208398",
     "exception": false,
     "start_time": "2023-02-22T14:58:52.915610",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(33.0, 0.5, 'Actual')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(c_matrix, annot=True, cmap='Blues',fmt='.3g')\n",
    "plt.xlabel(xlabel=\"Predicted\")\n",
    "plt.ylabel(ylabel=\"Actual\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7ac47d76",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.247945Z",
     "iopub.status.busy": "2023-02-22T14:58:53.247512Z",
     "iopub.status.idle": "2023-02-22T14:58:53.257398Z",
     "shell.execute_reply": "2023-02-22T14:58:53.256475Z"
    },
    "papermill": {
     "duration": 0.033546,
     "end_time": "2023-02-22T14:58:53.259500",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.225954",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "accu = (c_matrix[0][0] + c_matrix[1][1])/np.sum(c_matrix)\n",
    "sens = c_matrix[1][1]/(c_matrix[1][0]+c_matrix[1][1])\n",
    "fall = c_matrix[0][1]/(c_matrix[0][0]+c_matrix[0][1])\n",
    "spec = c_matrix[0][0]/(c_matrix[0][0]+c_matrix[0][1])\n",
    "misc = (c_matrix[0][1] + c_matrix[1][0])/np.sum(c_matrix)\n",
    "prec = c_matrix[1][1]/(c_matrix[1][1]+c_matrix[0][1])\n",
    "prev = (c_matrix[1][1] + c_matrix[1][0])/np.sum(c_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "cbcda246",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.296045Z",
     "iopub.status.busy": "2023-02-22T14:58:53.295581Z",
     "iopub.status.idle": "2023-02-22T14:58:53.302352Z",
     "shell.execute_reply": "2023-02-22T14:58:53.301287Z"
    },
    "papermill": {
     "duration": 0.028254,
     "end_time": "2023-02-22T14:58:53.305234",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.276980",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.64\n",
      "Sensitivity: 0.23\n",
      "Fall-out: 0.13\n",
      "Specificity: 0.87\n",
      "Misclassification Rate: 0.36\n",
      "Precision: 0.51\n",
      "Prevalence: 0.36\n"
     ]
    }
   ],
   "source": [
    "print(\"Accuracy: %.2f\" % accu)\n",
    "print(\"Sensitivity: %.2f\" % sens)\n",
    "print(\"Fall-out: %.2f\" % fall)\n",
    "print(\"Specificity: %.2f\" % spec)\n",
    "print(\"Misclassification Rate: %.2f\" % misc)\n",
    "print(\"Precision: %.2f\" % prec)\n",
    "print(\"Prevalence: %.2f\" % prev)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9088e0a0",
   "metadata": {
    "papermill": {
     "duration": 0.017273,
     "end_time": "2023-02-22T14:58:53.341501",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.324228",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Looking at the specificity we can see that our model is good to predict a negative result but the precision (true positive rate) shows that it does'n performed well on positive diagnostics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "5fa69483",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.379075Z",
     "iopub.status.busy": "2023-02-22T14:58:53.378609Z",
     "iopub.status.idle": "2023-02-22T14:58:53.394404Z",
     "shell.execute_reply": "2023-02-22T14:58:53.392452Z"
    },
    "papermill": {
     "duration": 0.038953,
     "end_time": "2023-02-22T14:58:53.398587",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.359634",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.67      0.87      0.76       246\n",
      "           1       0.51      0.23      0.32       138\n",
      "\n",
      "    accuracy                           0.64       384\n",
      "   macro avg       0.59      0.55      0.54       384\n",
      "weighted avg       0.61      0.64      0.60       384\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(y_test, my_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "283172b9",
   "metadata": {
    "papermill": {
     "duration": 0.017683,
     "end_time": "2023-02-22T14:58:53.436390",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.418707",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The recall and the f1 score aren't so good for the positive diagnosis like the Scikit Learning package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "ee8b3234",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.475007Z",
     "iopub.status.busy": "2023-02-22T14:58:53.474584Z",
     "iopub.status.idle": "2023-02-22T14:58:53.481834Z",
     "shell.execute_reply": "2023-02-22T14:58:53.480930Z"
    },
    "papermill": {
     "duration": 0.029363,
     "end_time": "2023-02-22T14:58:53.484152",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.454789",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "my_y_prob = [[],[]]\n",
    "for k in range(len(y_prob)):\n",
    "    if y_prob[k]<0.5:\n",
    "        my_y_prob[0].append(y_prob[k])\n",
    "    else:\n",
    "        my_y_prob[0].append(1 - y_prob[k])\n",
    "    if y_prob[k]>0.5:\n",
    "        my_y_prob[1].append(y_prob[k])\n",
    "    else:\n",
    "        my_y_prob[1].append(1 - y_prob[k])\n",
    "my_y_prob = np.array(my_y_prob).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "8ceeb6c9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.521883Z",
     "iopub.status.busy": "2023-02-22T14:58:53.521234Z",
     "iopub.status.idle": "2023-02-22T14:58:53.527952Z",
     "shell.execute_reply": "2023-02-22T14:58:53.526818Z"
    },
    "papermill": {
     "duration": 0.028446,
     "end_time": "2023-02-22T14:58:53.530418",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.501972",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(384, 2)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_y_prob.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3df06135",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.569961Z",
     "iopub.status.busy": "2023-02-22T14:58:53.569545Z",
     "iopub.status.idle": "2023-02-22T14:58:53.743759Z",
     "shell.execute_reply": "2023-02-22T14:58:53.742397Z"
    },
    "papermill": {
     "duration": 0.19742,
     "end_time": "2023-02-22T14:58:53.746568",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.549148",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "my_cdf = get_classes_cdf(y_test, my_y_prob[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "bde058b0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:53.785005Z",
     "iopub.status.busy": "2023-02-22T14:58:53.784605Z",
     "iopub.status.idle": "2023-02-22T14:58:54.178942Z",
     "shell.execute_reply": "2023-02-22T14:58:54.177900Z"
    },
    "papermill": {
     "duration": 0.416728,
     "end_time": "2023-02-22T14:58:54.181581",
     "exception": false,
     "start_time": "2023-02-22T14:58:53.764853",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualize the ROC curve\n",
    "fig = plt.figure(figsize = (10, 6))\n",
    "ax1 = plt.subplot()\n",
    "\n",
    "ax1.set_title(\"My model Cumulative Distribution Function (CDF)\")\n",
    "sns.lineplot(x = my_cdf['proba0'], y = my_cdf['cdf0'], color = 'b', ax = ax1, linewidth = 3)\n",
    "sns.lineplot(x = my_cdf['proba1'], y = my_cdf['cdf1'], color = 'g', ax = ax1, linewidth = 3)\n",
    "ax1.legend([\"class 0\", \"class 1\"])\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "08bc8698",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:54.220579Z",
     "iopub.status.busy": "2023-02-22T14:58:54.220156Z",
     "iopub.status.idle": "2023-02-22T14:58:54.234534Z",
     "shell.execute_reply": "2023-02-22T14:58:54.233013Z"
    },
    "papermill": {
     "duration": 0.037575,
     "end_time": "2023-02-22T14:58:54.237681",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.200106",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "My classifier:\n",
      "KS: 0.0530 (p-value: 9.505e-01)\n",
      "ROC AUC: 0.4895\n"
     ]
    }
   ],
   "source": [
    "print(\"My classifier:\")\n",
    "ks_my, auc_my = evaluate_ks_and_roc_auc(y_test, my_y_prob[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "733d5b1c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:54.277483Z",
     "iopub.status.busy": "2023-02-22T14:58:54.276684Z",
     "iopub.status.idle": "2023-02-22T14:58:54.283892Z",
     "shell.execute_reply": "2023-02-22T14:58:54.283043Z"
    },
    "papermill": {
     "duration": 0.029907,
     "end_time": "2023-02-22T14:58:54.286359",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.256452",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "logit_roc_auc = roc_auc_score(y_test, my_pred) \n",
    "fpr, tpr, thresholds = roc_curve(y_test, my_y_prob[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "b87ac92f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-02-22T14:58:54.326199Z",
     "iopub.status.busy": "2023-02-22T14:58:54.325354Z",
     "iopub.status.idle": "2023-02-22T14:58:54.573750Z",
     "shell.execute_reply": "2023-02-22T14:58:54.572607Z"
    },
    "papermill": {
     "duration": 0.271215,
     "end_time": "2023-02-22T14:58:54.576198",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.304983",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (12,8)) \n",
    "plt.plot(fpr, tpr, label='Logistic Regression (area = %0.2f)' % logit_roc_auc) \n",
    "plt.plot([0, 1], [0, 1],'r--') \n",
    "plt.text(0.5, 0.5, \"varying threshold scores (0-1)\", rotation=0, size=12,ha=\"center\", va=\"center\",bbox=dict(boxstyle=\"rarrow\"))\n",
    "plt.xlabel('False Positive Rate') \n",
    "plt.ylabel('True Positive Rate') \n",
    "plt.title('Receiver operating characteristic') \n",
    "plt.legend(loc=\"lower right\") \n",
    "#plt.savefig('Log_ROC') \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdca7ffe-e2eb-44dc-a77d-ffb06e32c66c",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "We build from scratch a logistic regression model and compared it to the scikit learn implementation default model. Our focus was in undestand the mechanisms behind the blackbox of logistic regression models and clear explain it. As expected for a didatic simple model, our implementation performed worse than the scikit learn model, but the objective of the tutorial was succesfully achieved. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca3c73c7",
   "metadata": {
    "papermill": {
     "duration": 0.019494,
     "end_time": "2023-02-22T14:58:54.615394",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.595900",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# References\n",
    "\n",
    "* [Logistic Regression - Wikipedia](https://en.wikipedia.org/wiki/Logistic_regression#Definition)\n",
    "* [Logistic Regression — Detailed Overview](https://towardsdatascience.com/logistic-regression-detailed-overview-46c4da4303bc)\n",
    "* [Logistic Regression Implementation](https://www.kaggle.com/code/kanncaa1/logistic-regression-implementation)\n",
    "* [Performance Measurement in Logistic Regresion](https://meettank29067.medium.com/performance-measurement-in-logistic-regression-8c9109b25278)\n",
    "* [Understanding AUC](https://medium.com/@data.science.enthusiast/auc-roc-curve-ae9180eaf4f7)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db393447",
   "metadata": {
    "papermill": {
     "duration": 0.019516,
     "end_time": "2023-02-22T14:58:54.654210",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.634694",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### If this notebook was helpful to you, consider to give an upvote! Thank you very much! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b6f77bd9",
   "metadata": {
    "papermill": {
     "duration": 0.019529,
     "end_time": "2023-02-22T14:58:54.693296",
     "exception": false,
     "start_time": "2023-02-22T14:58:54.673767",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 19.382942,
   "end_time": "2023-02-22T14:58:55.535972",
   "environment_variables": {},
   "exception": null,
   "input_path": "__notebook__.ipynb",
   "output_path": "__notebook__.ipynb",
   "parameters": {},
   "start_time": "2023-02-22T14:58:36.153030",
   "version": "2.3.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}