Logistic Regression-- Classification Performance Metrics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "bff422da",
   "metadata": {},
   "source": [
    "# Classification Performance Metrics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8be0d78",
   "metadata": {},
   "source": [
    "Confusion Metix Basics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "442a89c2",
   "metadata": {},
   "source": [
    "It is a measure of the overall classification performance of a machine learning model interpreted as the mean value of sensitivity for all possible values of specificity."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3edc1d5d",
   "metadata": {},
   "source": [
    "Accuracy Paradox"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "111b7b5e",
   "metadata": {},
   "source": [
    "Any classifier dealing with imbalanced classes has to confront the issue of the accuracy paradox."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b1363b2",
   "metadata": {},
   "source": [
    "Imbalanced classes will always result in distroted accuracy reflecting better performance than reflecting better performance than what is truly warranted."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21e356ba",
   "metadata": {},
   "source": [
    "Recall = (TP) / Total Actual Positives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c76f6e0b",
   "metadata": {},
   "source": [
    "Precision = (TP)/Total Predictive Positives"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71f18269",
   "metadata": {},
   "source": [
    "Recall and precision can help illuminate our performance specifically in regards to the relevent or positive cas."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f002578",
   "metadata": {},
   "source": [
    "Depending on the model, there is typically a trade off between precision and recall, which we will explore later on with the ROC curve."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80ce6b33",
   "metadata": {},
   "source": [
    "Since precision and recall are related to each other through the numerator(TP), We often also report the F1-Score, which is the harmonic mean of precision and recall.\n",
    "1. F = (2*precision * Recall)/ (precision+recall)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4a0386",
   "metadata": {},
   "source": [
    "The harmonic mean(instead of the normal mean) allows the entire precision or recall ends up being zero."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd07f0e1",
   "metadata": {},
   "source": [
    "# ROC curves"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8a229c7",
   "metadata": {},
   "source": [
    "An ROC curve (receiver operating characteristic curve) is a graph showing the performance of a classification model at all classification thresholds."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "339dbdfd",
   "metadata": {},
   "source": [
    "AUC - Area Under The Curve, Allows us to compare ROCs for different models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5aeb9295",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e2f77dba",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('hearing_test.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b44fe053",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>physical_score</th>\n",
       "      <th>test_result</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33.0</td>\n",
       "      <td>40.7</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>37.2</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>52.0</td>\n",
       "      <td>24.7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>56.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
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       "      <th>4</th>\n",
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       "    age  physical_score  test_result\n",
       "0  33.0            40.7            1\n",
       "1  50.0            37.2            1\n",
       "2  52.0            24.7            0\n",
       "3  56.0            31.0            0\n",
       "4  35.0            42.9            1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8bf1a8b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "X  = df.drop('test_result', axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "78bd8e2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = df['test_result']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a2d17200",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1ad7ea33",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "84be255c",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1, random_state=101)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0c2e8b06",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cc186761",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_X_train = scaler.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b85a5e06",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaled_X_test  = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bc8d5fe3",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "172167c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "log_model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "04c1d2a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_model.fit(scaled_X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a69d6a83",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.94953524,  3.45991194]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "fb0a36b4",
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>physical_score</th>\n",
       "      <th>test_result</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>33.0</td>\n",
       "      <td>40.7</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>50.0</td>\n",
       "      <td>37.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>52.0</td>\n",
       "      <td>24.7</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>56.0</td>\n",
       "      <td>31.0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>35.0</td>\n",
       "      <td>42.9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "    age  physical_score  test_result\n",
       "0  33.0            40.7            1\n",
       "1  50.0            37.2            1\n",
       "2  52.0            24.7            0\n",
       "3  56.0            31.0            0\n",
       "4  35.0            42.9            1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "27497d69",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import accuracy_score, confusion_matrix, classification_report"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "decefc9c",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred =log_model.predict(scaled_X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c11f52c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.93"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ec0e552f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[172,  21],\n",
       "       [ 14, 293]], dtype=int64)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "84e82dfb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import plot_confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "fd46b535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x2728742a1c0>"
      ]
     },
     "execution_count": 25,
     "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": [
    "plot_confusion_matrix(log_model,scaled_X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9b2c7c56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.confusion_matrix.ConfusionMatrixDisplay at 0x272883e6a60>"
      ]
     },
     "execution_count": 26,
     "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": [
    "plot_confusion_matrix(log_model,scaled_X_test, y_test, normalize='all')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "4f6a3634",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.92      0.89      0.91       193\n",
      "           1       0.93      0.95      0.94       307\n",
      "\n",
      "    accuracy                           0.93       500\n",
      "   macro avg       0.93      0.92      0.93       500\n",
      "weighted avg       0.93      0.93      0.93       500\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(y_test, y_pred))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "77c112c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import precision_score, recall_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0eaed70e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9331210191082803"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "precision_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fa3ba1d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9543973941368078"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "recall_score(y_test, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "f720a1b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import plot_precision_recall_curve, plot_roc_curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b4097a24",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.roc_curve.RocCurveDisplay at 0x27288ec1fa0>"
      ]
     },
     "execution_count": 32,
     "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": [
    "plot_roc_curve(log_model, scaled_X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8e86112a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.roc_curve.RocCurveDisplay at 0x2728984d940>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 2400x1600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax =plt.subplots(figsize = (12,8), dpi = 200)\n",
    "plot_roc_curve(log_model, scaled_X_test, y_test, ax = ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "f5034167",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<sklearn.metrics._plot.precision_recall_curve.PrecisionRecallDisplay at 0x27288de2820>"
      ]
     },
     "execution_count": 35,
     "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": [
    "plot_precision_recall_curve(log_model, scaled_X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "5920525e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02384343, 0.97615657])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_model.predict_proba(scaled_X_test)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7f071d86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4073f6ad",
   "metadata": {},
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}