3_classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "423da1fc",
   "metadata": {},
   "source": [
    "# Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5917efb5",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/insop/ML_crash_course/blob/main/3_classification.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2728b2cb",
   "metadata": {},
   "source": [
    "## Overview\n",
    "- recap from previous [notebook](https://github.com/insop/ML_crash_course/blob/main/2_linear_regression.ipynb)\n",
    "- classification logistic regression\n",
    "- example binary classification\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed3c7b82",
   "metadata": {},
   "source": [
    "## Recap from [previous notebook](https://github.com/insop/ML_crash_course/blob/main/2_linear_regression.ipynb)\n",
    "\n",
    "\n",
    "\n",
    "- how to form linear regression\n",
    "- how to measure goodness of the hypothesis? *loss function*\n",
    "- how to find the best parameters (weights)? *optimization*\n",
    "- gradient descent method, $w \\leftarrow w - \\eta$ $\\nabla$ Train_loss($W$) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78912f2a",
   "metadata": {},
   "source": [
    "## Classfiction task\n",
    "\n",
    "- predicts the class of output\n",
    "- binary classifier, output classes are 0 or 1\n",
    "- multi class classifier\n",
    "\n",
    "We will use binary classifier first, classifier takes input and produce scalar output.\n",
    "\n",
    "$x$ (input) $\\rightarrow$ $f$ (classifier)\n",
    "\n",
    "Based on the value, we can decide if the predicted output is 0 or 1.\n",
    "\n",
    "Multi class classification can be extended by using binary classfifcaiton.\n",
    "\n",
    "We will show an example of binary classifier using logistic regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4297d724",
   "metadata": {},
   "source": [
    "### Logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1af8c18",
   "metadata": {},
   "source": [
    "Logistic regression predicts binary values.\n",
    "For example, we have a dataset with one dimsnsion $x$ axis in the figure, which associated binary $y$ value. Linary regression could be considered as a predictor to fit; however, it is not sutible for the classification task. For example, if there is any outlier in the dataset, then the linear regression will not be a good predctor.\n",
    "\n",
    "Logistic regression uses fits *sigmoid* function to predict outputs.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "084478ae",
   "metadata": {},
   "source": [
    "<div>\n",
    "<img src=\"figures/log_reg.jpeg\" width=\"500\"/>\n",
    "</div>\n",
    "\n",
    "[Image source](https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148)\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83525287",
   "metadata": {},
   "source": [
    "Logistic regression is shown as follows:\n",
    "\n",
    "- sigmoid = $\\frac{1}{1+ \\exp-(x)}$\n",
    "\n",
    "- $z = W \\cdot \\phi(x)$\n",
    "    - $\\phi(x)$ is feature vector\n",
    "    - $W$ is weight vector\n",
    "- $\\hat y = sigmoid(z)$\n",
    "\n",
    "So here is a combined equation.\n",
    "\n",
    "- $\\hat y = \\frac{1}{1+ \\exp-(W \\cdot \\phi(x))}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08a8d5e4",
   "metadata": {},
   "source": [
    "Cost function is defined then we can use stochastic gradient to fit the funtion (See the references)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "416fbe87",
   "metadata": {},
   "source": [
    "## Classificaiton example with sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "3cfde1a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import colors\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from scipy.special import logit\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89b05507",
   "metadata": {},
   "source": [
    "### Load dataset, which include 2 features (2 exam scores), and admittance result.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "812198ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Admission data: \n",
    "# - exam 1 score (x1) \n",
    "# - exam 2 score (x2)\n",
    "# - admitted (y)\n",
    "\n",
    "data = np.loadtxt('datasets/ex2data1.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8d905b51",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separate features (x1, x2) from target (y)\n",
    "X, y = np.hsplit(data, np.array([2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "88e19ecb",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[34.62365962, 78.02469282],\n",
       "       [30.28671077, 43.89499752],\n",
       "       [35.84740877, 72.90219803],\n",
       "       [60.18259939, 86.3085521 ],\n",
       "       [79.03273605, 75.34437644],\n",
       "       [45.08327748, 56.31637178],\n",
       "       [61.10666454, 96.51142588],\n",
       "       [75.02474557, 46.55401354],\n",
       "       [76.0987867 , 87.42056972],\n",
       "       [84.43281996, 43.53339331]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "04c8f65e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.],\n",
       "       [0.],\n",
       "       [0.],\n",
       "       [1.],\n",
       "       [1.],\n",
       "       [0.],\n",
       "       [1.],\n",
       "       [1.],\n",
       "       [1.],\n",
       "       [1.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c82e34d6",
   "metadata": {},
   "source": [
    "### Good practice is to split train and test data. Train dataset is used to train model. Test dataset is used evaluate the final mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "388400a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# train test split\n",
    "\n",
    "# Split in training and testing\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "be7c8880",
   "metadata": {},
   "outputs": [],
   "source": [
    "# LogisticRegression estimator expect an y row vector\n",
    "y_train = y_train.squeeze()\n",
    "y_test = y_test.squeeze()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72091c1f",
   "metadata": {},
   "source": [
    "### We will use logictic regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6284f2c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1000000000.0)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define logistic regression\n",
    "\n",
    "# Parameter C is the inverse regularization strength (high values = low regularization).\n",
    "clf = LogisticRegression(C=1e9, solver='lbfgs')\n",
    "clf.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c7e8b510",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "theta: 0.27972459202295513, 0.22965356516269692, -31.195710016702105\n"
     ]
    }
   ],
   "source": [
    "# learned parameters\n",
    "\n",
    "theta0 = clf.intercept_[0]\n",
    "theta1 = clf.coef_[0,0]\n",
    "theta2 = clf.coef_[0,1]\n",
    "\n",
    "print(\"theta: {}, {}, {}\".format(theta2, theta1, theta0))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a11d15f5",
   "metadata": {},
   "source": [
    "### The following code cells for plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3941128f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computes x2 at y = logit(0.5) from x1 and model parameters\n",
    "# based on equation y = sigmoid(theta0 + theta1*x1 + theta2*x2)\n",
    "# logit(p) = log(p/(1-p)).\n",
    "# (used for computing the linear decision boundary)\n",
    "def x2(x1):\n",
    "    return (logit(0.5) - theta0 - theta1*x1) / theta2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bd02ce69",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1_min = X[:,0].min()\n",
    "x1_max = X[:,0].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "e9ba01e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# x1 and x2 data of linear decision boundary\n",
    "x1_plot = np.array([x1_min, x1_max])\n",
    "x2_plot = x2(x1_plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bb54dba",
   "metadata": {},
   "source": [
    "### Plot with training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c7046248",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124cda3d0>]"
      ]
     },
     "execution_count": 15,
     "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": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Mask for selecting positive and negative examples\n",
    "y_pos = y_train == 1\n",
    "y_neg = y_train == 0\n",
    "\n",
    "# Plot examples and decision boundary\n",
    "ax.plot(X_train[y_pos,0], X_train[y_pos,1], 'b+', label='Admitted')\n",
    "ax.plot(X_train[y_neg,0], X_train[y_neg,1], 'yo', label='Not admitted')\n",
    "ax.set_xlabel('Exam 1 score')\n",
    "ax.set_ylabel('Exam 2 score')\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "# Plot decision boundary\n",
    "ax.plot(x1_plot, x2_plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd3c63d",
   "metadata": {},
   "source": [
    "The accuracy of the model with training dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "9c743748",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9066666666666666"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Return the mean accuracy on the given test data and labels.\n",
    "\n",
    "clf.score(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1d162d70",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred=clf.predict(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0e31400",
   "metadata": {},
   "source": [
    "### Plot for test data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "18a273d3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x124de2ca0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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neH1xLKt2p1C7SiAv9mrM79vVxb+Mdd8YY7yDDUktRs3rVGHe4x3515OduKFSAOM+3UbfqWtYuuOwDWMt4WzymykJ7EzBg1SVb7cfZsqSWOKPnqN9g2pMuKMpHUKDnY5mPMCWyjC+ws4UHCIi3NmyNktejOTP97TkwPHzDJwew7B5PxB7+IzT8Ywx5jccKQoi8qKI7BCR7SKyQEQCRSRYRJaJSJz7tpoT2TyhbBk/HuoUwqqXevDS7U3YsO84faeuZszHW/n15AWn45lC8JY18I0pKsXefCQidYG1QDNVvSAiHwPfAM2A46o6WUQmANVUdXxur+XtzUfXcuLcJd6N3sO8mEQAHu3cgBE9GlKtQjmHk5nCsOYj4yu8sfnIHygvIv5AEHAQGADMc39/HnC3M9E8r1qFcrx8VzNWjo2if+s6vLduH5Gvr2Tayj2cv3TZ6XjGmFKs2IuCqv4KTAH2A4eAU6q6FKilqofcjzkE3JDT80VkuIhsEpFNKSkpxRXbI+pWLc+Uga1Z/EIkncKr88aSWLq/Ec38DYmkpWc4Hc/k08SJTicwpvCKvSi4+woGAGFAHaCCiDyc1+er6gxVjVDViJo1a3oqZrFqXKsSs4ZE8MnTXQgJDuLlz7fT563VfL3tkA1j9SHe0o/gLTmMb3Ki+agXsE9VU1Q1DfgMuAVIFpHaAO7bIw5kc1SH0GAWPt2FmY9G4O8njPjXFu6eto71e446Hc34kJyuO21MXjlRFPYDnUUkSEQE6An8AiwChrgfMwT40oFs+ZacPJ+YmFCio/2IiQklOXl+oV5PROjdrBaLX4jk9ftaceRMKg/N2sCj721k+6+niii1McbkzIk+hQ3AQmAL8LM7wwxgMtBbROKA3u5tr5acPJ/Y2OGkpiYCSmpqIrGxwwtdGADK+An3R9Rn5dgo/uvOpmw9cJJ+f1vLqAU/sv/Y+cKHNyWKDY01RcVmNBdCTEyouyBcKSCgAV26JBTpsU5dSGP6qr3MWbeP9AzloY4hjOzZiBoVA4r0OMb32dBY53n7Nb9tQTwPiY72A3L6/QlRUZ4ZPZR8+iJ//S6OjzcdINDfj2HdwnkyMpyKAf4eOZ7xPVYUnOft/wbeOE+hRAgICMnX/qJQq3Ig//f7lix9MZLIxjWZujyO7q+vZO66fVy6bMNYjQ2NNYVjRaEQwsNfxc8v6Ip9fn5BhIe/6vFj31SzIn9/uD2fP3sLjWpVZNK/d9LrzVV8+dOvZGR48UcU43He3GxRkpWUfh1rPiqk5OT5xMe/TGrqfgICQggPf5VatQYXawZVZdXuFF5bHMsvh07TrHZlxt/RlMhGNZDMv1CHeHvbqjGe4MvNR1YUSpCMDGXR1oNMWRpL0okLdAmvzoQ7mtK6flXHMnn7fw5jPMHb/+6tT6GU8PMT7m5bl+VjujPxd82ITT7DgGnreHb+ZuJTzjodz5hSw5f7dawolEAB/mUY2jWMVS9FMapnI6JjU+j91mr+6/OfOXL6osePX1LaVo0pKF/+W7fmo1Ig5Uwq76yIY/6G/fiXEZ64NYynut9E5cCyHj+2t59GG1MaFar5yL0cxZ9EZKZ7u5GI9CvqkMZzalYK4JUBLVg+pjt9mt3ItJV7iXx9JTNXx3MxLd3peMYYL5KX5qM5QCrQxb2dBPyvxxIZj2lQvQJvP9iWr0beSsu6VXj1m1+4bUo0n2w6QLqHhrH6ctuqMaXRdZuPRGSTqkaIyI+q2ta9b6uqti6WhLmw5qPCWbfnKJO/3cXPv56ica2KjLu9KT1vvsHxYazGGM8q7OijSyJSHvd6DiJyE64zB+PjujaswZcjuvLOQ225dDmDYf/cxMDpMWxKOO50NGOMQ/JSFCYCi4H6IjIfWA6M82gqU2z8/IR+reqwbHR3/vfuFiQcO89902MYNm8TcclnnI5njClmuTYfiYgfcB+uQtAZEOB7VfWKq75Y81HRO3/pMu+t3cf0VfGcv3SZe9vV48XejalTtbzT0YwxRaRQM5pFZLWqRnokWSFZUfCc4+cuMW3lHt6PSQSBx24J5dmom6gaVM7paMaYQipsUfgTcAH4CDiXuV9VHW94tqLgeUknzvPmst18/uOvVAzw55momxh6Sxjly5VxOpoxpoAKWxT25bBbVTW8KMIVhhWF4rPr8GleXxzLil1HqFU5gBd6NWZg+3r4l7FJ8cb4GlsQzxSZjfuOM/nbX9iy/yThNSsw7vYm3N78RhvGaowPKeyM5rIiMkpEFrq/nhMRz6+PYLxSx7BgPn3mFv7xSHv8RHj6gy3c8+56YvYeczqaMaYI5OXc/+9Ae+Bd91d7974CEZEmIvJTtq/TIvKCiASLyDIRiXPfVivoMYxniQi3N7+Rxc9347V7W3L41EUenPk9j83ZyM6Dp52OZ4wphLwUhQ6qOkRVV7i/hgIdCnpAVY1V1Taq2gZXgTkPfA5MAJaraiNcQ2AnFPQYpnj4l/HjgQ4hRL8UxR/uaMqWxBPc9bc1vPjRTxw4ft7peEXOl1e+zElJ+3lM0chLR/MWYKCq7nVvhwMLVbVdoQ8u0geYqKpdRSQWiFLVQyJSG4hW1Sa5Pd/6FLzLqfNp/H3VXuas20eGKoM7NWDkbQ2pXjHA6WhFoqSt+FrSfh6Td4UdfdQT16J48bgmrzUAhqrqyiII9h6wRVXfEZGTqlo12/dOqGquTUhWFLzToVMXmPpdHB9vOkBQOX+e7BbOsG5hVAjwdzpaoZS0N9GS9vOYvCtUR7OqLgcaAaPcX02KqCCUA/oDn+TzecNFZJOIbEpJSSlsDOMBtauUZ/K9rVj6YiRdG1bnre920/2NlfwzJoFLlzOcjpcvJe2CQUX58/jq78DkLi9nCiOA+ap60r1dDXhQVd8t1IFFBgAjVLWPe9uaj0qozYkneG3xLjbuO06D6kGM6dOEfi1r4+fnW8NYS9on68L+PCXt91GaFHaV1CczCwKAqp4AniyCXA8CC7JtLwKGuO8PAb4sgmMYL9C+QTU+Gt6ZOY91oHzZMoxa8CP9p61lTZyd6RnjbfJSFPwk28wkESkDFGoBHBEJAnoDn2XbPRnoLSJx7u9NLswxjHcREXo0vYGvR3Xjzftbc+JcGo/M3sjgWd+zLemk0/HypKRdMKggP09Ja04zv5WX5qM3gFBgOq5rKjwNHFDVMR5Pdx3WfOS7Ui+n88H3+3lnRRwnzqdxV6vajO3ThLAaFZyOZvLImo98V2FHH/kBw4FeuEYfLQVmqarjF/e1ouD7Tl9MY+bqeGat2UdaegaDOtZnVM9G3FAp0Olo5jqsKPiuwo4+ylDV6ap6H66+hBhvKAimZKgcWJYxfZqwalwUgzrW58ONB+j+ejR/WRrLmYtpTscrFr7a9FLSmtOMS17OFKJxDR31B34CUoBVqjra0+Gux84USp6Eo+eYsjSWr7YdolpQWZ67rREPdw4hwL/kLtVtn7hNcSvs6KMqqnoa+D0wR1Xb42pKMqbIhdaowDsPtePfz91K8zpV+H9f7eS2Kav4dHMS6Rn2zmmMp+WlKPi75w3cD3zl4TzGANCyXhU+GNaJ95/oSLUKZRnzyVbuensNK3Yl48vLvWeyUTzGW+Wl+Wgg8Cdgrao+61776A1Vvbc4AubGmo9Kh4wM5eufDzFlaSyJx87TMSyYCXc0pV1IyVhI15qPTHGzi+yYEuHS5Qw+/GE/f/4yjotcok+zWozr24SGN1RyOlqhWFEwxa2wfQrGeIVy/n482iWU3W/2YHTvxqzbc5Q+b61m/MJtHDp1wel4BWajeIw3sTMF43MyP1kfO5vKOyv38MH3ifiJ8FjXUJ7t3pAqQXZhQGNyY2cKxufl1DFbo1IAurk5K8ZEcWfL2sxYHU+311cwfdVeLqbZVBpjCiLXMwURaQrUBTao6tls+/uq6uJiyJcrO1Mona7VBr/z4GleX7KL6NgUbqwcyIu9G3Fvu3r4l7HPPsZkV6AzBREZhWul0pHAdvdS15n+XLQRjSm8ZnUqM3doRxY82ZlaVQIZ/+nP9J26hiU7DpeIYazGFIfcPkI9CbRX1buBKOBPIvK8+3u+tRC+KVGu1zHb5abqfPHsLUx/uB0Zqjz1/mbu/ft6NsQfK56AxviwazYfichOVW2WbbsisBDYCdymqm2KJWEurPnIXM/l9Aw+2ZzEX7/bTfLpVG5regPj+jah6Y2VnY5mjGMK2tF8WETaZG64+xT6ATWAlkWa0BgP8S/jx4MdQ4ge24PxfZvyQ8Jx7pi6htEf/0TSifNOxzPG6+R2plAPuKyqh3P4XldVXefpcNdjZwomv06ev8Tfo/cyZ30CKDzSpQEjejQkuEKhrhtljE+xGc3GXOXgyQv89bvdLNycRIVy/gyPDOeJbmEElfN3OpoxHmdFwZhriEs+w+tLYlm2M5malQIY1bMRgzrUp6wNYzUlmE1eM14nOXk+MTGhREf7ERMTSnLyfEdyNKpViZmPRvDpM10IrR7En77YTu83V/HVtoNk2FLdphTK85mCiFTGdaEdAFT1uKdC5ZWdKfim5OT5xMYOJyPjPx29fn5BNGkyg1q1BjuWS1VZ/ssRXl+yi93JZ2lVrwrj+zala8MajmUyxhMKdaYgIk+JSDKwDdjs/irUO7GIVBWRhSKyS0R+EZEuIhIsIstEJM59WzLWRTa/ER//8hUFASAj4zzx8S87lMhFROjVrBbfPh/JlIGtOXomlcGzNvDI7A1s//WUo9mMKS55aT4aCzRX1VBVDXN/hRfyuFOBxaraFGgN/AJMAJaraiNguXvblECpqfvztb+4lfET7mtfjxVjo/jjXTfz86+n6Pe3tYxc8COJx845Hc8Yj8pLUdgLFNmAbnczVCQwG0BVL6nqSWAAMM/9sHnA3UV1TONdAgJC8rXfKYFlyzCsWzirx/VgRI+bWLbzMD3/sor//nI7KWdSnY5njEfk5cprbYE5wAYg63+Cqo4q0AFdE+Jm4JoZ3RpXc9TzwK+qWjXb406o6m+akERkODAcICQkpH1iYmJBYhgHeWufwvUkn77I1OVxfPTDAQL8/RjWLZwnu4VRKdCW6ja+pVBDUkVkI7AW+BnIyNyvqvOu+aTcXy8C+B7oqqobRGQqcBoYmZeikJ11NPuu5OT5xMe/TGrqfgICQggPf9WrC0J28Sln+cvS3Xz98yGCK5Rj5G0NeahTCAH+ZZyOZkyeFLYorFfVW4owzI3A96oa6t7uhqv/oCEQpaqHRKQ2EK2qTXJ7LSsKxklbD5xk8re7iIk/Rr1q5RnTpzEDWtfFz8/WizTerbDzFFaKyHARqe0eIRQsIsEFDeNeNuOAiGS+4ffE1ZS0CBji3jcE17Ldxnit1vWr8q8nOzHv8Y5UDizLix9t5a6/rWVl7BFbqtv4rLycKezLYbcWZgSSu19hFlAOiAeG4ipQHwMhwH5g4PXmQtiZgvEWGRnKv7cdZMrSWA4cv0Dn8GDG921K2xAbWW28jy1zYUwxuXQ5gwUb9/P28jiOnbtE3+Y38lLfJtxUs6LT0YzJUuiiICItgGZAYOY+Vf1nkSUsICsKxludTb3MrDXxzFwdz8XLGdwfUY/nezbmxiqB13+yMR5W2I7mibiuvNYM+Aa4A1irqvcVcc58s6JgvN3Rs6m8s2IP8zckUsZPGNo1jKe730SV8jaM1TinsB3N9+HqDD6sqkNxzS0IKMJ8xpRYNSoGMKl/c5aPjuL25jfy9+i9RL6+khmr93IxLd3peMb8Rl6KwgVVzQAuu2cjHwEKu8yFMaVKSPUgpg5qy1cjb6V1/ar8+Ztd3DYlmo83HSDdVmM1XiQvRWGTiFQFZuKafbwF2OjJUMaUVC3qVuGfj3fkX8M6UbNSAOMWbuOOqatZtjPZhrEar5Cv0UciEgpUVtVtHkuUD9anYHyZqvLt9sNMWRJL/NFzRDSoxvg7mtIhtMDTgIzJk8Iunf1E5n1VTQB2uDufjTGFICLc2bI2S16M5NV7WrD/+HkGTo9h2LwfiD18xul4ppTKS/NRTxH5xj2juQWudYsqeTiXMaVG2TJ+DO7UgOiXonjp9iZsiD9O36mrGfvJVn49ecHpeKaUyes8hQeAabiW0H5QVdd5OlheWPORKYlOnLvEu9F7mLc+EQSGdGnAs1ENqVahnNPRTAlR2HkKjXBd3+Bn4GZc6xSNVtUiu8ZCQVlRMCXZrycv8Nay3Xy6JYmK5fx5OuomhnYNJaic//WfbEwuCjtP4d/An1T1KaA7EAf8UIT5jDE5qFu1PFMGtmbx85F0Cg/mjSWxRL0RzfwNiaSlZ1z/BYwpgLycKVRW1dNX7WukqnEeTZYHdqZgSpMfEo4z+dtdbE48QXiNCoy9vQl3tLgREVuq2+RPgc4URGQcgKqeFpGBV317aBHmM8bkYtIk122H0GAWPt2FmY9GUMZPeHb+Fu6eto71e486ms+ULNc8UxCRLara7ur7OW07xc4UTGkgAlf/N03PUD7dksRby3Zz6NRFIhvXZHzfJjSvU8WZkManFLRPQa5xP6dtY0wxKuMn3B9Rn5Vjo/ivO5uy9cBJ7np7Lc9/+CP7jzk+BsT4sNyKgl7jfk7bxpgiNGmS6wwhs7sg835mU1KmwLJlGB55E6vH9eCZqJtYsuMwPd+MZtKiHRw9m1rcsU0JkFvzUTpwDtdZQXlccxRwbweqquNr/1rzkSkNcmo+upbDpy4ydfluPt6URKC/H09GhjOsWzgVA2wYq/kPu/KaMT4sP0Uh054jZ5myJJbFOw5TvUI5RvVsxIMdQyjnn5dR6KakK+w8BWOMgyYWYKWxhjdUZPoj7fn82VtoeENFJi7aQa83V/HlT7+SYUt1m1w4cqYgIgnAGSAduKyqESISDHwEhAIJwP2qeiK317EzBWOuT1WJ3p3Ca9/uYtfhMzSvU5lxfZsS2aiGzXEopbz1TKGHqrbJFmwCsFxVGwHL3dvGByUnzycmJpToaD9iYkJJTp7vdKRSTUTo0eQGvhnVjbceaM2pC2kMeW8jg2dtYOuBk07HM17Gm5qPBuBaYwn37d2eOpC9aXlOcvJ8YmOHk5qaCCipqYnExg6337EX8PMT7mlbj+VjujPxd83YdfgMA6atY8T8LcSnnHU6nvESTjUf7QNO4Bra+g9VnSEiJ1W1arbHnFDVarm9TkGajzLftDIy/jOW288viCZNZlCr1uB8vZb5rZiYUHdBuFJAQAO6dEko/kDmms5cTGPmmn3MWhNP6uUMHuhQnxd6NuKGyoFORzMe5nWjj0SkjqoeFJEbgGXASGBRXoqCiAwHhgOEhIS0T0z87RtQbuxNy7Oio/3IeRqLEBVli7h5o5QzqfxtRRz/2rCfsmX8ePzWUJ7qfhOVAx0fdW48xOv6FFT1oPv2CPA50BFIFpHaAO7bI9d47gxVjVDViJo1a+b72Kmp+/O13+RPQEBIvvYb59WsFMD/DGjBd6O706tZLaat3Evk6yuZtSaei2npjma7erKe8bxiLwoiUkFEKmXeB/oA24FFwBD3w4YAX3ri+Pam5Vnh4a/i5xd0xT4/vyDCw191KJHJq9AaFfjbg235auSttKxbhf/9+hd6/mUVCzcnke7QMNZXXnHksKWaE2cKtYC1IrIV2Ah8raqLgclAbxGJA3q7t4ucvWl5Vq1ag2nSZAYBAQ0AISCggfXX+JgWdavw/hOdmD+sE8EVyjH2k63cOXUNy39Jxpcnu5q8KZUzmpOT5xMf/zKpqfsJCAghPPxVe9MyJgcZGco32w8xZUksCcfO0yG0GhPuaEr7BsEeO+akSTmfIUycaM1JRcXrOpqLirdNXrNiY0qqtPQMPvzhAFO/i+Po2VR6N6vFuNub0KhWJY8etyBLfJjrs6JQDGyoqykMX/lAcS71Mu+t3cc/Vsdz/tJl7mtfjxd6NaZO1fIeOZ4VBc/wutFHJVF8/MtXFASAjIzzxMe/7FAi4yt8acJfhQB/RvZsxOpxPXjsljC++PEgUVOi+b9vfuHk+UtFfryCrPtkCsfOFIqIjc83BeXLc2cOHD/PW9/t5vMff6VSgD/PRDXksVtCKV+ujNPRTC7sTKEY2FBXU1C+PHemfnAQb97fhm9GdSMiNJjXFu8iaspKFmzcz+V0+zDki6woFBEb6moKqiR8oLi5dmXee6wDHw3vTJ2q5fnDZz/T56+rWbz9kM8MY7WRTS5WFIqIjc83BVWSPlB0Cq/OZ8/cwj8eaY8AT3+whXveXc/38cecjnZdNlHOxfoUjPECvjL6KD8up2fw6ZYk3loWx+HTF4lqUpNxtzelWZ3KTkfLUWka6WRDUo0xjrmYls7c9Qm8u3IPZ1Ivc3ebuozu3Zj6wUHXf7KHldaJclYUjDGOO3U+jXdX7WHuugRUYXDnEJ7r0ZDqFQOcjgbYmULW96woGGOK06FTF5j6XRwfbzpAUDl/hkeG88StYVQI8Hc0lxUFF+toNsYUq9pVyjP53lYsfTGSrg2r8+ay3XR/I5r3YxJIc3AYq02Uc7EzBWOMozYnnuC1b3exMeE4DaoHMbZPE+5qWRs/P3E6WollZwrGGK/VvkE1PnqqM+89FkH5smUYueBH+k9by9q4o05HK5WsKBhjHCci3Na0Fl+P6sZfBrbmxLk0Hp69gYdnbeDnpFNOxytVrCgYY7xGGT/h3vb1WD6mO3+862Z2HDzF795Zy3P/2kLC0XNOxysVrE/BGOO1Tl9MY+bqeGat2UdaegYPdgxhZM+G3FAp0OloPs2GpBpjfNqR0xd5e0UcH248QNkyfgzrFsbwyHAqBZZ1OppPsqJgjCkR9h09x5SlsXy97RDBFcoxokdDHu4cQoC/LdWdHzb6yBhTIoTVqMC0h9qx6Lmu3Fy7Ev/vq53cNmUVn21JIj3Ddz/gehPHioKIlBGRH0XkK/d2sIgsE5E49201p7IZY7xbq3pVmT+sM+8/0ZFqFcoy+uOt3PX2GlbuOuIzS3V7KyfPFJ4Hfsm2PQFYrqqNgOXubWOMuaZujWqyaMStvP1gWy6kpTN07g88MON7tuw/4XQ0n+VIURCResBdwKxsuwcA89z35wF3F3MsY4wP8vMT+reuw7IXu/M/A5oTn3KW37+7nqfe38SeI2edjudzHOloFpGFwP8BlYCxqtpPRE6qatVsjzmhqr9pQhKR4cBwgJCQkPaJib+9tq0xpvQ6l3qZ2Wv38Y9Ve7mQls79EfV5oVdjbqxiw1gzeVVHs4j0A46o6uaCPF9VZ6hqhKpG1KxZs4jTGWN8XYUAf0b1bMTqcT0Yckson25JovsbK5n87S5OnU9zOp7Xc6L5qCvQX0QSgA+B20TkAyBZRGoDuG+POJDNGFNCVK8YwMTfNWfFmCjubFmbf6zeS+QbK/nHqr1cTEt3Op7XcnSegohE8Z/mozeAY6o6WUQmAMGqOi6359s8BWNMXu08eJrXl+wiOjaF2lUCebFXY37fri7+ZUrfyHyvaj7KxWSgt4jEAb3d28YYUySa1anM3KEdWfBkZ26oHMi4T7fRd+oaluw4bMNYs7EZzcaYUkdVWbLjMK8vjiX+6DnahVRlwh030zEs2OloxcJXzhSMMaZYiAh9W9Rm6YuR/N/vW5J04gL3/yOGx+f+wK7Dp52O5yg7UzDGlHoXLqUzZ/0+/h69l7Opl7mnbV1G925MvWpBTkfzCFsQzxhj8uDk+Uu8G72XuesTQOGRLg0Y0aMhwRXKOR2tSFlRMMaYfDh48gJvLdvNp1uSqFDOn6e6h/P4rWEElfN3OlqRsKJgjDEFsDv5DG8siWXZzmRqVgrg+Z6NeKBDfcr6+DBW62g2xpgCaFyrEjMfjWDh010IrR7EH7/YTp+3VvP1tkMldhirFQVjjLmOiNBgPn6qC7MejaBsGWHEv7YwYNo61u856nS0ImdFwRhj8kBE6NWsFt8+H8mUga05eiaVh2Zt4JHZG9j+6ymn4xUZ61MwxpgCuJiWzgffJ/LOyj2cPJ9G/9Z1GNOnMQ2qV3A62nVZR7MxxnjIqQtpzFi9l9lr93E5XRncKYTnbmtEzUoBTke7JisKxhjjYcmnLzJ1eRwf/XCAAH8/hnULZ3hkOBUDvG8YqxUFY4wpJntTzvKXpbF88/Nhqlcox3O3NeShTiEE+JdxOloWG5JqjDHF5KaaFXl3cHu+GNGVxrUq8cq/d9LrzVV88eOvZGR4/4dwKwrGGOMBbepX5V9PdmLe4x2pGFCWFz76ibv+tpbo2CNePcfBioIxxniIiNC9cU2+HnkrUwe14WxqGo/N+YEHZ37PTwdOOh0vR1YUjDHGw/z8hAFt6rJ8dBSTfteMuOSz3D1tHc98sJm9KWedjncF62g2xphidjb1MjNXxzNrTTwXL2dwf0R9XujViFqVA4vl+Db6yBhjvNDRs6m8s2IP8zckUsZPeLxrGE91v4kq5ct69LhWFIwxxovtP3aevyyL5cufDlI1qCwjohrySJcGBJb1zDBWKwrGGOMDtv96iteXxLJ6dwp1qgTyYu/G/L5dPcr4SZEex6vmKYhIoIhsFJGtIrJDRF5x7w8WkWUiEue+rVbc2Ywxxkkt6lbhn4935F/DOlGjUgAvLdzGHVNXs2xncrENY3Vi9FEqcJuqtgbaAH1FpDMwAViuqo2A5e5tY4wpdW5pWIMvR3Rl2kPtSEtXnvznJgZOj2FTwnGPH7vYi4K6ZI7BKuv+UmAAMM+9fx5wd3FnM8YYbyEi3NWqNktfjOTVe1qQePw8902PYdi8TexOPuO54zrRpyAiZYDNQENgmqqOF5GTqlo122NOqOpvmpBEZDgwHCAkJKR9YmJiMaU2xhjnnL90mTnrEpgevZdzly7zeNcw/tivWYFey6v6FABUNV1V2wD1gI4i0iIfz52hqhGqGlGzZk2PZTTGGG8SVM6fET0asnpcDx7vGkb94CCPHMfRNV1V9aSIRAN9gWQRqa2qh0SkNnDEyWzGGOONqlUoV+AzhLxwYvRRTRGp6r5fHugF7AIWAUPcDxsCfFnc2YwxprRz4kyhNjDP3a/gB3ysql+JSAzwsYg8AewHBjqQzRhjSrViLwqqug1om8P+Y0DP4s5jjDHmP2yVVGOMMVmsKBhjjMliRcEYY0wWKwrGGGOyWFEwxhiTxaeXzhaRFKCg61zUAI4WYRxPs7ye40tZwbfy+lJWKD15G6hqjktC+HRRKAwR2XSttT+8keX1HF/KCr6V15eyguUFaz4yxhiTjRUFY4wxWUpzUZjhdIB8srye40tZwbfy+lJWsLylt0/BGGPMb5XmMwVjjDFXsaJgjDEmS6koCiISKCIbRWSriOwQkVfc+4NFZJmIxLlvf3P5T6eISBkR+VFEvnJve3PWBBH5WUR+EpFN7n3enLeqiCwUkV0i8ouIdPHGvCLSxP07zfw6LSIveGPWTCLyovv/2HYRWeD+v+eVeUXkeXfOHSLygnuf12QVkfdE5IiIbM+275r5ROQPIrJHRGJF5PaCHrdUFAUgFbhNVVsDbYC+ItIZmAAsV9VGwHL3trd4Hvgl27Y3ZwXooaptso2Z9ua8U4HFqtoUaI3r9+x1eVU11v07bQO0B84Dn+OFWQFEpC4wCohQ1RZAGWAQXpjXfQngJ4GOuP4G+olII7wr61xcV6XMLsd8ItIM1++6ufs577qvWZN/qlqqvoAgYAvQCYgFarv31wZinc7nzlLP/Q9+G/CVe59XZnXnSQBqXLXPK/MClYF9uAdZeHvebPn6AOu8OStQFzgABOO6VstX7txelxfXRbxmZdv+EzDO27ICocD2bNs55gP+APwh2+OWAF0KcszScqaQ2RzzE65rPy9T1Q1ALVU9BOC+vcHBiNn9FdcfaEa2fd6aFUCBpSKyWUSGu/d5a95wIAWY426emyUiFfDevJkGAQvc970yq6r+CkzBdeXEQ8ApVV2Kd+bdDkSKSHURCQLuBOrjnVmzu1a+zIKcKcm9L99KTVFQ1XR1nYbXAzq6Tx+9joj0A46o6mans+RDV1VtB9wBjBCRSKcD5cIfaAf8XVXbAufwguaM3IhIOaA/8InTWXLjbt8eAIQBdYAKIvKws6lypqq/AK8By4DFwFbgsqOhCkdy2Feg+QalpihkUtWTQDSudrdkEakN4L494lyyLF2B/iKSAHwI3CYiH+CdWQFQ1YPu2yO42rw74r15k4Ak95kiwEJcRcJb84Kr2G5R1WT3trdm7QXsU9UUVU0DPgNuwUvzqupsVW2nqpHAcSAOL82azbXyJeE608lUDzhYkAOUiqIgIjVFpKr7fnlcf7y7gEXAEPfDhgBfOhIwG1X9g6rWU9VQXE0GK1T1YbwwK4CIVBCRSpn3cbUhb8dL86rqYeCAiDRx7+oJ7MRL87o9yH+ajsB7s+4HOotIkIgIrt/tL3hpXhG5wX0bAvwe1+/YK7Nmc618i4BBIhIgImFAI2BjgY7gdIdPMXXWtAJ+BLbhesP6b/f+6rg6dOPct8FOZ70qdxT/6Wj2yqy42ui3ur92AC97c153tjbAJvffwxdANW/Ni2tgxDGgSrZ9XpnVne0VXB+4tgPvAwHemhdYg+sDwVagp7f9bnEVqUNAGq4zgSdyywe8DOzF1Rl9R0GPa8tcGGOMyVIqmo+MMcbkjRUFY4wxWawoGGOMyWJFwRhjTBYrCsYYY7JYUTAlkoikX7XCaLHNWs5pdUtjfIUNSTUlkoicVdWKDh07EjgL/FNdq4UWxzHLqGp6cRzLlGx2pmBKDRGp4l5rvol7e4GIPOm+/3cR2STZrrfh3p8gIn8WkRj399uJyBIR2SsiT+d0HFVdjWvZhNyyDHSv5b9VRFa795URkSniujbFNhEZ6d7f071438/us5CAbNn+W0TWAgNFpI875xYR+UREHCmKxrdZUTAlVfmrmo8eUNVTwHPAXBEZBFRT1Znux7+srmtBtAK6i0irbK91QFW74JoBOxe4D+gM/E8h8v03cLu6rvHR371vOK7F5NqqaitgvogEuo/5gKq2xLWg3zPZXueiqt4KfAf8EeilrsUJNwGjC5HPlFL+TgcwxkMuqGtV3Cuo6jIRGQhMw3VxlUz3u5f99se1Tn0zXMtggGtdGYCfgYqqegY4IyIXRaSquhZZzK91uIrTx7gWjgPXmlzTVfWyO+txEWmNa5G53e7HzANG4FpeHeAj921nd+Z1rmWHKAfEFCCXKeWsKJhSRUT8gJuBC7guBpPkXkBsLNBBVU+IyFwgMNvTUt23GdnuZ24X6P+Qqj4tIp2Au4CfRKQNruWPr+7ky2lJ5OzOZXvcMlV9sCB5jMlkzUemtHkR18qdDwLviUhZXFdjOwecEpFauJaq9igRuUlVN6jqfwNHcS17vBR4WkT83Y8JxrW4XKiINHQ/9RFgVQ4v+T3QNfNx7pVKG3v65zAlj50pmJKqvPtKe5kWA+8Bw4COqnrG3cH7R1WdKCI/4lrlNR5X006BicgCXCvc1hCRJGCiqs6+6mFviOuawIJrtcutuFYWbQxsE5E0YKaqviMiQ4FP3MXiB2D61cdU1RQReQxYkNkRjauPYffVjzUmNzYk1RhjTBZrPjLGGJPFioIxxpgsVhSMMcZksaJgjDEmixUFY4wxWawoGGOMyWJFwRhjTJb/D5mMgTwf14pAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Mask for selecting positive and negative examples\n",
    "y_pos = y_test == 1\n",
    "y_neg = y_test == 0\n",
    "\n",
    "# Plot examples and decision boundary\n",
    "ax.plot(X_test[y_pos,0], X_test[y_pos,1], 'b+', label='Admitted')\n",
    "ax.plot(X_test[y_neg,0], X_test[y_neg,1], 'yo', label='Not admitted')\n",
    "ax.set_xlabel('Exam 1 score')\n",
    "ax.set_ylabel('Exam 2 score')\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "# Plot decision boundary\n",
    "ax.plot(x1_plot, x2_plot)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a258e2a",
   "metadata": {},
   "source": [
    "The accuracy of the mode with test dataset (held out dataset), which is used for measuring final model performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6fb47fe4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.84"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Return the mean accuracy on the given test data and labels.\n",
    "\n",
    "clf.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4160e3da",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_test_pred=clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9b380a2",
   "metadata": {},
   "source": [
    "### Precision\n",
    "\n",
    "Precision = $\\frac{TP}{TP+FP}$, among predicted to be true (TP+FP), how many of them are true (TP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ca1f18e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import precision_score, recall_score\n",
    "\n",
    "precision_score(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dd5b55c",
   "metadata": {},
   "source": [
    "### Recall\n",
    "\n",
    "Recall = $\\frac{TP}{TP+FN}$, among real true (TP+FN), how many of them are true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f032c4bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.875"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeeeaabe",
   "metadata": {},
   "source": [
    "### F1 score\n",
    "\n",
    "F1 score = $\\frac{2}{\\frac{1}{precision}+\\frac{1}{recall}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "7785db0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9032258064516129"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import f1_score\n",
    "\n",
    "f1_score(y_test, y_test_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4021b799",
   "metadata": {},
   "source": [
    "### Confusion matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "318aae7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 8,  1],\n",
       "       [ 2, 14]])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "cm = confusion_matrix(y_test, y_test_pred)\n",
    "cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "bc7aafee",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "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": [
    "import seaborn as sns\n",
    "\n",
    "ax = sns.heatmap(cm, annot=True, cmap='Blues')\n",
    "\n",
    "ax.set_title('Seaborn Confusion Matrix with labels\\n\\n');\n",
    "ax.set_xlabel('\\nPredicted Values')\n",
    "ax.set_ylabel('Actual Values ');\n",
    "\n",
    "## Ticket labels - List must be in alphabetical order\n",
    "ax.xaxis.set_ticklabels(['False','True'])\n",
    "ax.yaxis.set_ticklabels(['False','True'])\n",
    "\n",
    "## Display the visualization of the Confusion Matrix.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f1f5f72",
   "metadata": {},
   "source": [
    "## Summary\n",
    "- review classification\n",
    "- classification example\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d15c2b0a",
   "metadata": {},
   "source": [
    "## Credits\n",
    "\n",
    "This notebook uses the contents from the followring materials:\n",
    "\n",
    "1. Chapter 2 from Book [Hands-on Machine Learning with Scikit-Learn, Keras and TensorFlow](https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/)\n",
    "1. [Example code from https://github.com/krasserm](https://github.com/krasserm/machine-learning-notebooks/blob/1a0b8b65a0d2013af0e0b304e792199be2e54973/ml-ex2.ipynb)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eae186cf",
   "metadata": {},
   "source": [
    "## References\n",
    "1. [logistic regression review 1](https://towardsdatascience.com/logistic-regression-detailed-overview-46c4da4303bc)\n",
    "1. [logistic regression review 2](https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0c874636",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.12 ('pytorch_env')",
   "language": "python",
   "name": "python3812jvsc74a57bd03fa8f9c45b60853bb3d615f814548b5337da45fc6ea40b493b018f80b808d764"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}