Logistic regression - ROC study .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "# roc curve and auc score\n",
    "from sklearn.datasets import make_classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Select the Right Threshold values using ROC Curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X, y = make_classification(n_samples=2000, n_classes=2, weights=[1,1], random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 20)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, ..., 1, 1, 0])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train,X_test,y_train,y_test = train_test_split(X, y, test_size=0.3, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve\n",
    "from sklearn.metrics import roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RF train roc-auc: 1.0\n",
      "RF test roc-auc: 0.9811166666666666\n"
     ]
    }
   ],
   "source": [
    "## Apply RandomForestClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "rf_model = RandomForestClassifier()\n",
    "rf_model.fit(X_train, y_train)\n",
    "ytrain_pred = rf_model.predict_proba(X_train)\n",
    "print('RF train roc-auc: {}'.format(roc_auc_score(y_train, ytrain_pred[:,1])))\n",
    "ytest_pred = rf_model.predict_proba(X_test)\n",
    "print('RF test roc-auc: {}'.format(roc_auc_score(y_test, ytest_pred[:,1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.  , 0.  ],\n",
       "       [0.96, 0.04],\n",
       "       [0.02, 0.98],\n",
       "       ...,\n",
       "       [0.97, 0.03],\n",
       "       [0.96, 0.04],\n",
       "       [0.24, 0.76]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ytrain_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logistic train roc-auc: 0.9863568922694498\n",
      "Logistic test roc-auc: 0.9885777777777777\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_classifier=LogisticRegression()\n",
    "log_classifier.fit(X_train, y_train)\n",
    "ytrain_pred = log_classifier.predict_proba(X_train)\n",
    "print('Logistic train roc-auc: {}'.format(roc_auc_score(y_train, ytrain_pred[:,1])))\n",
    "ytest_pred = log_classifier.predict_proba(X_test)\n",
    "print('Logistic test roc-auc: {}'.format(roc_auc_score(y_test, ytest_pred[:,1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adaboost train roc-auc: 0.9975081174960356\n",
      "Adaboost test roc-auc: 0.9826111111111111\n"
     ]
    }
   ],
   "source": [
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "ada_classifier=AdaBoostClassifier()\n",
    "ada_classifier.fit(X_train, y_train)\n",
    "ytrain_pred = ada_classifier.predict_proba(X_train)\n",
    "print('Adaboost train roc-auc: {}'.format(roc_auc_score(y_train, ytrain_pred[:,1])))\n",
    "ytest_pred = ada_classifier.predict_proba(X_test)\n",
    "print('Adaboost test roc-auc: {}'.format(roc_auc_score(y_test, ytest_pred[:,1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adaboost train roc-auc: 0.981670071491109\n",
      "Adaboost test roc-auc: 0.9426111111111111\n"
     ]
    }
   ],
   "source": [
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn_classifier=KNeighborsClassifier()\n",
    "knn_classifier.fit(X_train, y_train)\n",
    "ytrain_pred = knn_classifier.predict_proba(X_train)\n",
    "print('Adaboost train roc-auc: {}'.format(roc_auc_score(y_train, ytrain_pred[:,1])))\n",
    "ytest_pred = knn_classifier.predict_proba(X_test)\n",
    "print('Adaboost test roc-auc: {}'.format(roc_auc_score(y_test, ytest_pred[:,1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ensemble test roc-auc: 0.9843555555555554\n"
     ]
    }
   ],
   "source": [
    "#Now we will focus on selecting the best threshold for maximum accuracy\n",
    "pred=[]\n",
    "for model in [rf_model,log_classifier,ada_classifier,knn_classifier]:\n",
    "    pred.append(pd.Series(model.predict_proba(X_test)[:,1]))\n",
    "final_prediction=pd.concat(pred,axis=1).mean(axis=1)\n",
    "print('Ensemble test roc-auc: {}'.format(roc_auc_score(y_test,final_prediction)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.99</td>\n",
       "      <td>0.991861</td>\n",
       "      <td>0.559186</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.000008</td>\n",
       "      <td>0.463282</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.966929</td>\n",
       "      <td>0.538202</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.94</td>\n",
       "      <td>0.761539</td>\n",
       "      <td>0.509875</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.64</td>\n",
       "      <td>0.779443</td>\n",
       "      <td>0.490344</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>595</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.024239</td>\n",
       "      <td>0.461121</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>596</th>\n",
       "      <td>0.02</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>0.441377</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>597</th>\n",
       "      <td>0.99</td>\n",
       "      <td>0.984385</td>\n",
       "      <td>0.532403</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>598</th>\n",
       "      <td>0.01</td>\n",
       "      <td>0.001147</td>\n",
       "      <td>0.441720</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>599</th>\n",
       "      <td>0.98</td>\n",
       "      <td>0.989540</td>\n",
       "      <td>0.559890</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>600 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0         1         2    3\n",
       "0    0.99  0.991861  0.559186  1.0\n",
       "1    0.01  0.000008  0.463282  0.0\n",
       "2    1.00  0.966929  0.538202  0.8\n",
       "3    0.94  0.761539  0.509875  0.8\n",
       "4    0.64  0.779443  0.490344  0.4\n",
       "..    ...       ...       ...  ...\n",
       "595  0.02  0.024239  0.461121  0.0\n",
       "596  0.02  0.000003  0.441377  0.0\n",
       "597  0.99  0.984385  0.532403  1.0\n",
       "598  0.01  0.001147  0.441720  0.2\n",
       "599  0.98  0.989540  0.559890  0.8\n",
       "\n",
       "[600 rows x 4 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat(pred,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0.885262\n",
       "1      0.118323\n",
       "2      0.826283\n",
       "3      0.752853\n",
       "4      0.577447\n",
       "         ...   \n",
       "595    0.126340\n",
       "596    0.115345\n",
       "597    0.876697\n",
       "598    0.163217\n",
       "599    0.832357\n",
       "Length: 600, dtype: float64"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.90938114, 0.90938114, 0.90422166, 0.90327475, 0.81139369,\n",
       "       0.8105558 , 0.80225303, 0.80162833, 0.78387064, 0.78321156,\n",
       "       0.77242916, 0.77037124, 0.7266922 , 0.72637362, 0.70971721,\n",
       "       0.70893711, 0.6717442 , 0.66993537, 0.61238185, 0.59550386,\n",
       "       0.58745356, 0.57925354, 0.57646627, 0.57486186, 0.56406376,\n",
       "       0.56389283, 0.54365858, 0.52377948, 0.52105932, 0.48116892,\n",
       "       0.4396034 , 0.37975652, 0.37629719, 0.35568654, 0.35086612,\n",
       "       0.23717239, 0.23390421, 0.20666474, 0.20598417, 0.11788782,\n",
       "       0.1178351 , 0.10632697])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#### Calculate the ROc Curve\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(y_test, final_prediction)\n",
    "thresholds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>thresholds</th>\n",
       "      <th>accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.439603</td>\n",
       "      <td>0.961667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.481169</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.523779</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.543659</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.521059</td>\n",
       "      <td>0.956667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    thresholds  accuracy\n",
       "30    0.439603  0.961667\n",
       "29    0.481169  0.958333\n",
       "27    0.523779  0.958333\n",
       "26    0.543659  0.958333\n",
       "28    0.521059  0.956667"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "accuracy_ls = []\n",
    "for thres in thresholds:\n",
    "    y_pred = np.where(final_prediction>thres,1,0)\n",
    "    accuracy_ls.append(accuracy_score(y_test, y_pred, normalize=True))\n",
    "    \n",
    "accuracy_ls = pd.concat([pd.Series(thresholds), pd.Series(accuracy_ls)],\n",
    "                        axis=1)\n",
    "accuracy_ls.columns = ['thresholds', 'accuracy']\n",
    "accuracy_ls.sort_values(by='accuracy', ascending=False, inplace=True)\n",
    "accuracy_ls.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>thresholds</th>\n",
       "      <th>accuracy</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.439603</td>\n",
       "      <td>0.961667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.481169</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.523779</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.543659</td>\n",
       "      <td>0.958333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.521059</td>\n",
       "      <td>0.956667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.563893</td>\n",
       "      <td>0.955000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.564064</td>\n",
       "      <td>0.953333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.574862</td>\n",
       "      <td>0.951667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.576466</td>\n",
       "      <td>0.950000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.579254</td>\n",
       "      <td>0.948333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.379757</td>\n",
       "      <td>0.946667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.587454</td>\n",
       "      <td>0.946667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0.376297</td>\n",
       "      <td>0.945000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.612382</td>\n",
       "      <td>0.943333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>0.355687</td>\n",
       "      <td>0.943333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.595504</td>\n",
       "      <td>0.943333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0.350866</td>\n",
       "      <td>0.941667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.669935</td>\n",
       "      <td>0.935000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.671744</td>\n",
       "      <td>0.933333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.708937</td>\n",
       "      <td>0.920000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.709717</td>\n",
       "      <td>0.918333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.726374</td>\n",
       "      <td>0.910000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.726692</td>\n",
       "      <td>0.908333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.233904</td>\n",
       "      <td>0.876667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0.237172</td>\n",
       "      <td>0.876667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0.206665</td>\n",
       "      <td>0.848333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>0.205984</td>\n",
       "      <td>0.846667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.770371</td>\n",
       "      <td>0.846667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.772429</td>\n",
       "      <td>0.845000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.783212</td>\n",
       "      <td>0.833333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.783871</td>\n",
       "      <td>0.831667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.801628</td>\n",
       "      <td>0.810000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.802253</td>\n",
       "      <td>0.808333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.810556</td>\n",
       "      <td>0.793333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.811394</td>\n",
       "      <td>0.791667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0.117888</td>\n",
       "      <td>0.595000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0.117835</td>\n",
       "      <td>0.593333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.903275</td>\n",
       "      <td>0.511667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.904222</td>\n",
       "      <td>0.510000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.106327</td>\n",
       "      <td>0.501667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.909381</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.909381</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    thresholds  accuracy\n",
       "30    0.439603  0.961667\n",
       "29    0.481169  0.958333\n",
       "27    0.523779  0.958333\n",
       "26    0.543659  0.958333\n",
       "28    0.521059  0.956667\n",
       "25    0.563893  0.955000\n",
       "24    0.564064  0.953333\n",
       "23    0.574862  0.951667\n",
       "22    0.576466  0.950000\n",
       "21    0.579254  0.948333\n",
       "31    0.379757  0.946667\n",
       "20    0.587454  0.946667\n",
       "32    0.376297  0.945000\n",
       "18    0.612382  0.943333\n",
       "33    0.355687  0.943333\n",
       "19    0.595504  0.943333\n",
       "34    0.350866  0.941667\n",
       "17    0.669935  0.935000\n",
       "16    0.671744  0.933333\n",
       "15    0.708937  0.920000\n",
       "14    0.709717  0.918333\n",
       "13    0.726374  0.910000\n",
       "12    0.726692  0.908333\n",
       "36    0.233904  0.876667\n",
       "35    0.237172  0.876667\n",
       "37    0.206665  0.848333\n",
       "38    0.205984  0.846667\n",
       "11    0.770371  0.846667\n",
       "10    0.772429  0.845000\n",
       "9     0.783212  0.833333\n",
       "8     0.783871  0.831667\n",
       "7     0.801628  0.810000\n",
       "6     0.802253  0.808333\n",
       "5     0.810556  0.793333\n",
       "4     0.811394  0.791667\n",
       "39    0.117888  0.595000\n",
       "40    0.117835  0.593333\n",
       "3     0.903275  0.511667\n",
       "2     0.904222  0.510000\n",
       "41    0.106327  0.501667\n",
       "1     0.909381  0.500000\n",
       "0     1.909381  0.500000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_ls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def plot_roc_curve(fpr, tpr):\n",
    "    plt.plot(fpr, tpr, color='orange', label='ROC')\n",
    "    plt.plot([0, 1], [0, 1], color='darkblue', linestyle='--')\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "    plt.title('Receiver Operating Characteristic (ROC) Curve')\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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