| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 246, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.066585Z", | |
| "start_time": "2024-12-02T22:49:28.004988Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "source": [ | |
| " <div style=\"display:block;width:100%;margin:auto;\" direction=rtl align=center><br><br>\n", | |
| " <div style=\"width:100%;margin:100;display:block;background-color:#fff0;\" display=block align=center>\n", | |
| " <table style=\"border-style:hidden;border-collapse:collapse;\"> <tr>\n", | |
| " <td style=\"border: none!important;\">\n", | |
| " <img width=130 align=right src=\"https://i.ibb.co/yXKQmtZ/logo1.png\" style=\"margin:0;\" />\n", | |
| " </td>\n", | |
| " <td style=\"text-align:center;border: none!important;\">\n", | |
| " <h1 align=center><font size=5 color=\"#025F5F\"> <b>Machine Learning</b><br><br>Project 2 Intruduction to Machine learning </i></font></h1>\n", | |
| " </td>\n", | |
| " <td style=\"border: none!important;\">\n", | |
| " <img width=170 align=left src=\"https://i.ibb.co/wLjqFkw/logo2.png\" style=\"margin:0;\" />\n", | |
| " </td>\n", | |
| " </tr>\n", | |
| " </table>\n", | |
| " </div>\n", | |
| "</div>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "collapsed": false | |
| }, | |
| "source": [ | |
| "Mohammad Taha Majlesi - 810101504\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.738130Z", | |
| "start_time": "2024-12-02T22:49:28.071948Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Decision Boundary (Threshold): x = 3.0\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "\n", | |
| "mu1 = 2\n", | |
| "sigma1 = 1\n", | |
| "mu2 = 4\n", | |
| "sigma2 = 1\n", | |
| "pi1 = 0.5\n", | |
| "pi2 = 0.5\n", | |
| "\n", | |
| "n_samples = 100 \n", | |
| "\n", | |
| "np.random.seed(10)\n", | |
| "\n", | |
| "classes = np.random.choice([0, 1], size=n_samples, p=[pi1, pi2])\n", | |
| "\n", | |
| "mu = np.array([mu1, mu2])\n", | |
| "sigma = np.array([sigma1, sigma2])\n", | |
| "\n", | |
| "X = np.random.normal(mu[classes], sigma[classes])\n", | |
| "\n", | |
| "y_true = classes\n", | |
| "\n", | |
| "x1 = X[classes == 0]\n", | |
| "x2 = X[classes == 1]\n", | |
| "\n", | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.scatter(x1, np.zeros_like(x1), color='blue', alpha=0.6, label='Class 1')\n", | |
| "plt.scatter(x2, np.zeros_like(x2), color='red', alpha=0.6, label='Class 2')\n", | |
| "plt.title('Scatter Plot of Samples from Class 1 and Class 2')\n", | |
| "plt.xlabel('Feature x')\n", | |
| "plt.yticks([])\n", | |
| "plt.legend()\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n", | |
| "\n", | |
| "threshold = (mu1 + mu2) / 2\n", | |
| "print(f\"Decision Boundary (Threshold): x = {threshold}\")\n", | |
| "\n", | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.scatter(x1, np.zeros_like(x1), color='blue', alpha=0.6, label='Class 1')\n", | |
| "plt.scatter(x2, np.zeros_like(x2), color='red', alpha=0.6, label='Class 2')\n", | |
| "plt.axvline(x=threshold, color='green', linestyle='--', label=f'Decision Boundary (x={threshold})')\n", | |
| "plt.title('Scatter Plot with Decision Boundary')\n", | |
| "plt.xlabel('Feature x')\n", | |
| "plt.yticks([])\n", | |
| "plt.legend()\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n", | |
| "\n", | |
| "def classify(x, threshold):\n", | |
| " return np.where(x >= threshold, 1, 0)\n", | |
| "\n", | |
| "y_pred = classify(X, threshold)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.754383Z", | |
| "start_time": "2024-12-02T22:49:28.687087Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Decision Boundary (Threshold): x = 3.0\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "threshold = (mu1 + mu2) / 2\n", | |
| "print(f\"Decision Boundary (Threshold): x = {threshold}\")\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.769179Z", | |
| "start_time": "2024-12-02T22:49:28.694465Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def classify(x, threshold):\n", | |
| " return np.where(x >= threshold, 1, 0)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.770231Z", | |
| "start_time": "2024-12-02T22:49:28.702726Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Confusion Matrix:\n", | |
| "[[40 11]\n", | |
| " [ 7 42]]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "tp = fp = tn = fn = 0\n", | |
| "\n", | |
| "for true_label, pred_label in zip(y_true, y_pred):\n", | |
| " if true_label == 1 and pred_label == 1:\n", | |
| " tp += 1 \n", | |
| " elif true_label == 0 and pred_label == 1:\n", | |
| " fp += 1\n", | |
| " elif true_label == 0 and pred_label == 0:\n", | |
| " tn += 1 \n", | |
| " elif true_label == 1 and pred_label == 0:\n", | |
| " fn += 1 \n", | |
| "\n", | |
| "confusion_matrix = np.array([[tn, fp],\n", | |
| " [fn, tp]])\n", | |
| "\n", | |
| "print(\"Confusion Matrix:\")\n", | |
| "print(confusion_matrix)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.943129Z", | |
| "start_time": "2024-12-02T22:49:28.711229Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Confusion Matrix:\n", | |
| "[[42 11]\n", | |
| " [ 7 42]]\n", | |
| "Accuracy: 0.82\n", | |
| "Precision (Positive Class): 0.79\n", | |
| "Recall (Positive Class): 0.86\n", | |
| "F1-Score (Positive Class): 0.82\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "confusion_mat = np.array([[tp, fp],\n", | |
| " [fn, tp]])\n", | |
| "\n", | |
| "accuracy = (tp + tn) / (tp + tn + fp + fn)\n", | |
| "\n", | |
| "precision = tp / (tp + fp) if (tp + fp) > 0 else 0\n", | |
| "recall = tp / (tp + fn) if (tp + fn) > 0 else 0\n", | |
| "f1_score = 2 * (precision * recall) / (precision + recall) if (precision + recall) > 0 else 0\n", | |
| "\n", | |
| "\n", | |
| "print(\"Confusion Matrix:\")\n", | |
| "print(confusion_mat)\n", | |
| "\n", | |
| "print(f\"Accuracy: {accuracy:.2f}\")\n", | |
| "print(f\"Precision (Positive Class): {precision:.2f}\")\n", | |
| "print(f\"Recall (Positive Class): {recall:.2f}\")\n", | |
| "print(f\"F1-Score (Positive Class): {f1_score:.2f}\")\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.945138Z", | |
| "start_time": "2024-12-02T22:49:28.718868Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "[ 5.10770823 2.24454398 3.93808797 3.24610704 2.71195902 2.91826915\n", | |
| " 1.51790686 4.08958761 2.82699862 0.04548788 4.11747566 2.09254311\n", | |
| " 1.07709074 4.46975143 3.85563324 3.59986165 3.70401615 2.84820861\n", | |
| " 4.70683045 3.21273107 4.29294072 1.52919275 4.40432561 3.26064326\n", | |
| " 1.68717124 1.65111808 3.56097376 4.14110417 4.27304932 2.38142925\n", | |
| " 3.42688664 2.67955245 5.23620533 4.46532508 3.38323223 2.34623312\n", | |
| " 3.02251611 4.16681027 3.65671662 4.66788961 3.77005336 2.87044881\n", | |
| " 1.3600374 4.31383052 0.77416402 3.77820686 3.33992631 4.02930971\n", | |
| " 3.98538575 3.4471656 1.71237059 0.64068943 3.95195867 1.51921266\n", | |
| " 2.37775309 5.61440797 2.87689596 1.61127205 4.33234995 3.13497317\n", | |
| " 4.51071441 4.41429764 5.34454942 4.49351532 1.76299582 2.05728515\n", | |
| " 1.29292855 2.54666484 2.94250041 1.02040323 3.21814885 1.94347928\n", | |
| " 2.46088845 4.66237401 -0.29510333 0.80407069 3.66689884 3.20860923\n", | |
| " 4.27417278 1.48509008 2.2889288 4.61229731 5.10012937 2.56435253\n", | |
| " 1.28720056 1.73914052 2.54842807 2.60319905 5.00686114 3.70557399\n", | |
| " 0.57911948 1.32105323 2.53388481 4.7439744 4.22504964 2.11718142\n", | |
| " 4.24461452 1.82270118 1.59427047 4.78177519]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "def discriminant_score(x):\n", | |
| " term1 = -((x - mu1)**2) / (2 * sigma1**2) + np.log(pi1)\n", | |
| " term2 = -((x - mu2)**2) / (2 * sigma2**2) + np.log(pi2)\n", | |
| " return term1 - term2\n", | |
| "\n", | |
| "scores = discriminant_score(X)\n", | |
| "print(X)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.946868Z", | |
| "start_time": "2024-12-02T22:49:28.736464Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "[-6.22881595 -5.22881595 -4.68909885 -4.47241065 -4.21541647 -4.20025875\n", | |
| " -4.01372228 -3.56355038 -3.48794881 -3.41366091 -3.33577922 -3.32474802\n", | |
| " -3.22459462 -3.02142882 -2.98703063 -2.93950287 -2.93065016 -2.82859528\n", | |
| " -2.80865121 -2.6646999 -2.62766104 -2.58588145 -2.54834556 -2.54609864\n", | |
| " -2.48922904 -2.45009928 -2.33362053 -2.28220834 -2.23495132 -2.17917523\n", | |
| " -2.05861942 -1.97077149 -1.90391735 -1.87617594 -1.71126647 -1.55641373\n", | |
| " -1.54010671 -1.41114799 -1.40803229 -1.33379768 -1.31343325 -1.1997233\n", | |
| " -1.12194753 -0.8943312 -0.85377328 -0.76646446 -0.67985262 -0.52128652\n", | |
| " -0.49221408 -0.4362977 -0.42546215 -0.41721846 -0.26994635 -0.04503221\n", | |
| " 0.11499918 0.1634617 0.24620807 0.25910239 0.30358278 0.34600275\n", | |
| " 0.57608197 0.64089509 0.7936019 0.87129495 0.90314387 0.90667032\n", | |
| " 0.93223038 1.0782231 1.2371415 1.24449383 1.30753377 1.42214239\n", | |
| " 1.51091205 1.76563716 1.81491378 1.8854297 2.11304145 2.35459765\n", | |
| " 2.47400837 2.52171896 2.57525883 2.62565751 2.69776384 2.77745589\n", | |
| " 2.81145906 2.9416145 2.96157468 2.96418628 3.02981984 3.27992521\n", | |
| " 3.35789355 3.41414289 3.42559887 3.84581853 3.95919354 4.39185862\n", | |
| " 4.45167196 4.71862115 4.84176103 5.90902424 6.59020666 7.59020666]\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "49\n", | |
| "51\n", | |
| "[1.0, 1.0, 0.9795918367346939, 0.9591836734693877, 0.9387755102040817, 0.9183673469387755, 0.8979591836734694, 0.8775510204081632, 0.8571428571428571, 0.8367346938775511, 0.8163265306122449, 0.7959183673469388, 0.7755102040816326, 0.7551020408163265, 0.7346938775510204, 0.7142857142857143, 0.6938775510204082, 0.6938775510204082, 0.673469387755102, 0.673469387755102, 0.6530612244897959, 0.6326530612244898, 0.6122448979591837, 0.5918367346938775, 0.5714285714285714, 0.5510204081632653, 0.5510204081632653, 0.5306122448979592, 0.5102040816326531, 0.4897959183673469, 0.46938775510204084, 0.4489795918367347, 0.4489795918367347, 0.42857142857142855, 0.40816326530612246, 0.3877551020408163, 0.3673469387755102, 0.3469387755102041, 0.32653061224489793, 0.30612244897959184, 0.2857142857142857, 0.2857142857142857, 0.2653061224489796, 0.24489795918367346, 0.24489795918367346, 0.22448979591836735, 0.22448979591836735, 0.22448979591836735, 0.20408163265306123, 0.1836734693877551, 0.1836734693877551, 0.16326530612244897, 0.14285714285714285, 0.14285714285714285, 0.14285714285714285, 0.14285714285714285, 0.14285714285714285, 0.12244897959183673, 0.10204081632653061, 0.10204081632653061, 0.10204081632653061, 0.10204081632653061, 0.08163265306122448, 0.08163265306122448, 0.08163265306122448, 0.08163265306122448, 0.08163265306122448, 0.08163265306122448, 0.08163265306122448, 0.061224489795918366, 0.061224489795918366, 0.061224489795918366, 0.04081632653061224, 0.04081632653061224, 0.04081632653061224, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.02040816326530612, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n", | |
| "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.9803921568627451, 0.9803921568627451, 0.9607843137254902, 0.9607843137254902, 0.9607843137254902, 0.9607843137254902, 0.9607843137254902, 0.9607843137254902, 0.9607843137254902, 0.9411764705882353, 0.9411764705882353, 0.9411764705882353, 0.9411764705882353, 0.9411764705882353, 0.9411764705882353, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9215686274509803, 0.9019607843137255, 0.9019607843137255, 0.9019607843137255, 0.8823529411764706, 0.8823529411764706, 0.8627450980392157, 0.8431372549019608, 0.8431372549019608, 0.8431372549019608, 0.8235294117647058, 0.8235294117647058, 0.8235294117647058, 0.803921568627451, 0.7843137254901961, 0.7647058823529411, 0.7450980392156863, 0.7450980392156863, 0.7450980392156863, 0.7254901960784313, 0.7058823529411765, 0.6862745098039216, 0.6862745098039216, 0.6666666666666666, 0.6470588235294118, 0.6274509803921569, 0.6078431372549019, 0.5882352941176471, 0.5686274509803921, 0.5686274509803921, 0.5490196078431373, 0.5294117647058824, 0.5294117647058824, 0.5098039215686274, 0.49019607843137253, 0.49019607843137253, 0.47058823529411764, 0.45098039215686275, 0.43137254901960786, 0.4117647058823529, 0.39215686274509803, 0.37254901960784315, 0.35294117647058826, 0.3333333333333333, 0.3137254901960784, 0.29411764705882354, 0.27450980392156865, 0.2549019607843137, 0.23529411764705882, 0.21568627450980393, 0.19607843137254902, 0.17647058823529413, 0.1568627450980392, 0.13725490196078433, 0.11764705882352941, 0.11764705882352941, 0.09803921568627451, 0.0784313725490196, 0.058823529411764705, 0.0392156862745098, 0.0196078431372549, 0.0]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "sorted_scores = np.sort(scores)\n", | |
| "thresholds = np.concatenate(([sorted_scores[0] - 1], sorted_scores, [sorted_scores[-1] + 1]))\n", | |
| "print(thresholds)\n", | |
| "\n", | |
| "tpr_list = []\n", | |
| "fpr_list = []\n", | |
| "\n", | |
| "for tau in thresholds:\n", | |
| " y_pred_tau = np.where(scores >= tau, 1, 0)\n", | |
| " \n", | |
| " tp_tau = np.sum((y_true == 1) & (y_pred_tau == 1))\n", | |
| " fp_tau = np.sum((y_true == 0) & (y_pred_tau == 1))\n", | |
| " tn_tau = np.sum((y_true == 0) & (y_pred_tau == 0))\n", | |
| " fn_tau = np.sum((y_true == 1) & (y_pred_tau == 0))\n", | |
| " \n", | |
| " tpr = tp_tau / (tp_tau + fn_tau) if (tp_tau + fn_tau) > 0 else 0\n", | |
| " fpr = fp_tau / (fp_tau + tn_tau) if (fp_tau + tn_tau) > 0 else 0\n", | |
| "\n", | |
| " tpr_list.append(tpr)\n", | |
| " fpr_list.append(fpr)\n", | |
| "print(tpr_list)\n", | |
| "print(fpr_list)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:28.974320Z", | |
| "start_time": "2024-12-02T22:49:28.744818Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Area Under the ROC Curve (AUROC): 0.11\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "fpr_array = np.array(fpr_list)\n", | |
| "tpr_array = np.array(tpr_list)\n", | |
| "\n", | |
| "sorted_indices = np.argsort(fpr_array)\n", | |
| "fpr_array = fpr_array[sorted_indices]\n", | |
| "tpr_array = tpr_array[sorted_indices]\n", | |
| "\n", | |
| "auroc = np.trapz(tpr_array, fpr_array)\n", | |
| "\n", | |
| "print(f\"Area Under the ROC Curve (AUROC): {auroc:.2f}\")\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.042597Z", | |
| "start_time": "2024-12-02T22:49:28.769321Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 800x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.figure(figsize=(8, 6))\n", | |
| "plt.plot(tpr_array,fpr_array, color='darkorange', lw=2,\n", | |
| " label=f'ROC curve (AUROC = {auroc:.2f})')\n", | |
| "plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n", | |
| "plt.title('ROC Curve')\n", | |
| "plt.xlabel('False Positive Rate')\n", | |
| "plt.ylabel('True Positive Rate')\n", | |
| "plt.legend(loc=\"lower right\")\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 18, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.628294Z", | |
| "start_time": "2024-12-02T22:49:28.968711Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "New Decision Boundary (Threshold): x = 4.10\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 1000x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Confusion Matrix with New Priors:\n", | |
| "[[89 3]\n", | |
| " [ 2 6]]\n", | |
| "Accuracy: 0.95\n", | |
| "Precision (Positive Class): 0.67\n", | |
| "Recall (Positive Class): 0.75\n", | |
| "F1-Score (Positive Class): 0.71\n", | |
| "Area Under the ROC Curve (AUROC) with New Priors: 0.09\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": "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", | |
| "text/plain": [ | |
| "<Figure size 800x600 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "\n", | |
| "mu1 = 2\n", | |
| "sigma1 = 1\n", | |
| "mu2 = 4\n", | |
| "sigma2 = 1\n", | |
| "pi1_new = 0.9\n", | |
| "pi2_new = 0.1\n", | |
| "\n", | |
| "n_samples = 100\n", | |
| "\n", | |
| "np.random.seed(10)\n", | |
| "\n", | |
| "classes_new = np.random.choice([0, 1], size=n_samples, p=[pi1_new, pi2_new])\n", | |
| "\n", | |
| "mu = np.array([mu1, mu2])\n", | |
| "sigma = np.array([sigma1, sigma2])\n", | |
| "\n", | |
| "X_new = np.random.normal(mu[classes_new], sigma[classes_new])\n", | |
| "\n", | |
| "y_true_new = classes_new\n", | |
| "\n", | |
| "x1_new = X_new[classes_new == 0]\n", | |
| "x2_new = X_new[classes_new == 1]\n", | |
| "\n", | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.scatter(x1_new, np.zeros_like(x1_new), color='blue', alpha=0.6, label='Class 1')\n", | |
| "plt.scatter(x2_new, np.zeros_like(x2_new), color='red', alpha=0.6, label='Class 2')\n", | |
| "plt.title('Scatter Plot of Samples from Class 1 and Class 2 (New Priors)')\n", | |
| "plt.xlabel('Feature x')\n", | |
| "plt.yticks([])\n", | |
| "plt.legend()\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n", | |
| "\n", | |
| "sigma = sigma1\n", | |
| "threshold_new = ((mu1 + mu2) / 2) + (sigma**2 / (mu2 - mu1)) * np.log(pi1_new / pi2_new)\n", | |
| "print(f\"New Decision Boundary (Threshold): x = {threshold_new:.2f}\")\n", | |
| "\n", | |
| "plt.figure(figsize=(10, 6))\n", | |
| "plt.scatter(x1_new, np.zeros_like(x1_new), color='blue', alpha=0.6, label='Class 1')\n", | |
| "plt.scatter(x2_new, np.zeros_like(x2_new), color='red', alpha=0.6, label='Class 2')\n", | |
| "plt.axvline(x=threshold_new, color='purple', linestyle='--',\n", | |
| " label=f'New Decision Boundary (x={threshold_new:.2f})')\n", | |
| "plt.title('Scatter Plot with New Decision Boundary')\n", | |
| "plt.xlabel('Feature x')\n", | |
| "plt.yticks([])\n", | |
| "plt.legend()\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n", | |
| "\n", | |
| "def classify(x, threshold):\n", | |
| " return np.where(x >= threshold, 1, 0)\n", | |
| "\n", | |
| "y_pred_new = classify(X_new, threshold_new)\n", | |
| "\n", | |
| "TP = FP = TN = FN = 0\n", | |
| "\n", | |
| "for true_label, pred_label in zip(y_true_new, y_pred_new):\n", | |
| " if true_label == 1 and pred_label == 1:\n", | |
| " TP += 1\n", | |
| " elif true_label == 0 and pred_label == 1:\n", | |
| " FP += 1\n", | |
| " elif true_label == 0 and pred_label == 0:\n", | |
| " TN += 1\n", | |
| " elif true_label == 1 and pred_label == 0:\n", | |
| " FN += 1\n", | |
| "\n", | |
| "confusion_mat_new = np.array([[TN, FP],\n", | |
| " [FN, TP]])\n", | |
| "\n", | |
| "print(\"Confusion Matrix with New Priors:\")\n", | |
| "print(confusion_mat_new)\n", | |
| "\n", | |
| "total = TP + TN + FP + FN\n", | |
| "\n", | |
| "accuracy_new = (TP + TN) / total\n", | |
| "\n", | |
| "precision_new = TP / (TP + FP) if (TP + FP) > 0 else 0\n", | |
| "recall_new = TP / (TP + FN) if (TP + FN) > 0 else 0\n", | |
| "f1_score_new = 2 * (precision_new * recall_new) / (precision_new + recall_new) if (precision_new + recall_new) > 0 else 0\n", | |
| "\n", | |
| "print(f\"Accuracy: {accuracy_new:.2f}\")\n", | |
| "print(f\"Precision (Positive Class): {precision_new:.2f}\")\n", | |
| "print(f\"Recall (Positive Class): {recall_new:.2f}\")\n", | |
| "print(f\"F1-Score (Positive Class): {f1_score_new:.2f}\")\n", | |
| "\n", | |
| "def discriminant_score_new(x):\n", | |
| " term1 = -((x - mu1)**2) / (2 * sigma1**2) + np.log(pi1_new)\n", | |
| " term2 = -((x - mu2)**2) / (2 * sigma2**2) + np.log(pi2_new)\n", | |
| " return term1 - term2\n", | |
| "\n", | |
| "scores_new = discriminant_score_new(X_new)\n", | |
| "\n", | |
| "thresholds = np.sort(np.unique(scores_new))\n", | |
| "thresholds = np.concatenate(([scores_new.min() - 1], thresholds, [scores_new.max() + 1]))\n", | |
| "\n", | |
| "tpr_list = []\n", | |
| "fpr_list = []\n", | |
| "\n", | |
| "for thresh in thresholds:\n", | |
| " y_pred_thresh = np.where(scores_new >= thresh, 1, 0)\n", | |
| " \n", | |
| " TP = np.sum((y_true_new == 1) & (y_pred_thresh == 1))\n", | |
| " FP = np.sum((y_true_new == 0) & (y_pred_thresh == 1))\n", | |
| " TN = np.sum((y_true_new == 0) & (y_pred_thresh == 0))\n", | |
| " FN = np.sum((y_true_new == 1) & (y_pred_thresh == 0))\n", | |
| " \n", | |
| " TPR = TP / (TP + FN) if (TP + FN) > 0 else 0 # True Positive Rate\n", | |
| " FPR = FP / (FP + TN) if (FP + TN) > 0 else 0 # False Positive Rate\n", | |
| " \n", | |
| " tpr_list.append(TPR)\n", | |
| " fpr_list.append(FPR)\n", | |
| "\n", | |
| "tpr_array = np.array(tpr_list)\n", | |
| "fpr_array = np.array(fpr_list)\n", | |
| "\n", | |
| "sorted_indices = np.argsort(fpr_array)\n", | |
| "fpr_array = fpr_array[sorted_indices]\n", | |
| "tpr_array = tpr_array[sorted_indices]\n", | |
| "\n", | |
| "auroc_new = np.trapz(tpr_array, fpr_array)\n", | |
| "\n", | |
| "print(f\"Area Under the ROC Curve (AUROC) with New Priors: {auroc_new:.2f}\")\n", | |
| "\n", | |
| "plt.figure(figsize=(8, 6))\n", | |
| "plt.plot(tpr_array,fpr_array, color='darkorange', lw=2,\n", | |
| " label=f'ROC curve (AUROC = {auroc_new:.2f})')\n", | |
| "plt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--')\n", | |
| "plt.title('ROC Curve with New Priors')\n", | |
| "plt.xlabel('False Positive Rate')\n", | |
| "plt.ylabel('True Positive Rate')\n", | |
| "plt.legend(loc=\"lower right\")\n", | |
| "plt.grid(True)\n", | |
| "plt.show()\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 256, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.629629Z", | |
| "start_time": "2024-12-02T22:49:29.622024Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 256, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.630098Z", | |
| "start_time": "2024-12-02T22:49:29.625604Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 256, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.631905Z", | |
| "start_time": "2024-12-02T22:49:29.628949Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 256, | |
| "metadata": { | |
| "ExecuteTime": { | |
| "end_time": "2024-12-02T22:49:29.638791Z", | |
| "start_time": "2024-12-02T22:49:29.632217Z" | |
| }, | |
| "collapsed": false | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "pythonProject1", | |
| "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": "3.11.5" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } | |
Xet Storage Details
- Size:
- 257 kB
- Xet hash:
- cc2bea618e65e3039172a5f0a9d7cebcc9bf3edc0dfc0d7bad408e8cb245ffe8
·
Xet efficiently stores files, intelligently splitting them into unique chunks and accelerating uploads and downloads. More info.