Logistic_regression.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",
    "import seaborn as sns\n",
    "from sklearn.metrics import accuracy_score \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"C:\\\\Users\\\\Siddharth Bingi\\\\Documents\\\\Sabir ML\\\\Assignment 1\\\\sgemm_product_dataset\\\\sgemm_product.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>MWG</th>\n",
       "      <th>NWG</th>\n",
       "      <th>KWG</th>\n",
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       "      <th>STRM</th>\n",
       "      <th>STRN</th>\n",
       "      <th>SA</th>\n",
       "      <th>SB</th>\n",
       "      <th>Run1 (ms)</th>\n",
       "      <th>Run2 (ms)</th>\n",
       "      <th>Run3 (ms)</th>\n",
       "      <th>Run4 (ms)</th>\n",
       "      <th>avg_run</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>115.26</td>\n",
       "      <td>115.87</td>\n",
       "      <td>118.55</td>\n",
       "      <td>115.80</td>\n",
       "      <td>116.3700</td>\n",
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       "      <td>1</td>\n",
       "      <td>78.13</td>\n",
       "      <td>78.25</td>\n",
       "      <td>79.25</td>\n",
       "      <td>79.19</td>\n",
       "      <td>78.7050</td>\n",
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       "      <td>79.84</td>\n",
       "      <td>80.69</td>\n",
       "      <td>80.76</td>\n",
       "      <td>80.97</td>\n",
       "      <td>80.5650</td>\n",
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       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>16</td>\n",
       "      <td>16</td>\n",
       "      <td>16</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>84.32</td>\n",
       "      <td>89.90</td>\n",
       "      <td>86.75</td>\n",
       "      <td>85.58</td>\n",
       "      <td>86.6375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>16</td>\n",
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       "      <td>16</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
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       "      <td>0</td>\n",
       "      <td>115.13</td>\n",
       "      <td>121.98</td>\n",
       "      <td>122.73</td>\n",
       "      <td>114.81</td>\n",
       "      <td>118.6625</td>\n",
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       "   MWG  NWG  KWG  MDIMC  NDIMC  MDIMA  NDIMB  KWI  VWM  VWN  STRM  STRN  SA  \\\n",
       "0   16   16   16      8      8      8      8    2    1    1     0     0   0   \n",
       "1   16   16   16      8      8      8      8    2    1    1     0     0   0   \n",
       "2   16   16   16      8      8      8      8    2    1    1     0     0   1   \n",
       "3   16   16   16      8      8      8      8    2    1    1     0     0   1   \n",
       "4   16   16   16      8      8      8      8    2    1    1     0     1   0   \n",
       "\n",
       "   SB  Run1 (ms)  Run2 (ms)  Run3 (ms)  Run4 (ms)   avg_run  \n",
       "0   0     115.26     115.87     118.55     115.80  116.3700  \n",
       "1   1      78.13      78.25      79.25      79.19   78.7050  \n",
       "2   0      79.84      80.69      80.76      80.97   80.5650  \n",
       "3   1      84.32      89.90      86.75      85.58   86.6375  \n",
       "4   0     115.13     121.98     122.73     114.81  118.6625  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"avg_run\"] = df.iloc[:,14:].mean(axis = 1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "median_run = df['avg_run'].median()\n",
    "df.loc[df['avg_run'] >= median_run, 'run_class'] = 1\n",
    "df.loc[df['avg_run'] < median_run, 'run_class'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MWG</th>\n",
       "      <th>NWG</th>\n",
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       "      <th>MDIMC</th>\n",
       "      <th>NDIMC</th>\n",
       "      <th>MDIMA</th>\n",
       "      <th>NDIMB</th>\n",
       "      <th>KWI</th>\n",
       "      <th>VWM</th>\n",
       "      <th>VWN</th>\n",
       "      <th>STRM</th>\n",
       "      <th>STRN</th>\n",
       "      <th>SA</th>\n",
       "      <th>SB</th>\n",
       "      <th>run_class</th>\n",
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       "      <td>0</td>\n",
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       "      <td>8</td>\n",
       "      <td>8</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>16</td>\n",
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       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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      "text/plain": [
       "   MWG  NWG  KWG  MDIMC  NDIMC  MDIMA  NDIMB  KWI  VWM  VWN  STRM  STRN  SA  \\\n",
       "0   16   16   16      8      8      8      8    2    1    1     0     0   0   \n",
       "1   16   16   16      8      8      8      8    2    1    1     0     0   0   \n",
       "2   16   16   16      8      8      8      8    2    1    1     0     0   1   \n",
       "3   16   16   16      8      8      8      8    2    1    1     0     0   1   \n",
       "4   16   16   16      8      8      8      8    2    1    1     0     1   0   \n",
       "\n",
       "   SB  run_class  \n",
       "0   0        1.0  \n",
       "1   1        1.0  \n",
       "2   0        1.0  \n",
       "3   1        1.0  \n",
       "4   0        1.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop(['Run1 (ms)', 'Run2 (ms)','Run3 (ms)', 'Run4 (ms)', 'avg_run'], axis = 1, inplace = True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining feature matrix(X) and response vector(y) \n",
    "X = df.iloc[:, 0:14]\n",
    "y = df[\"run_class\"]\n",
    "  \n",
    "\n",
    "\n",
    "# splitting X and y into training and testing sets \n",
    "from sklearn.model_selection import train_test_split \n",
    "from sklearn.linear_model import LinearRegression\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, \n",
    "                                                    random_state=10) \n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_test = scaler.fit_transform(X_test)\n",
    "one_column = np.ones((X_test.shape[0],1))\n",
    "X_test = np.concatenate((one_column, X_test), axis = 1)\n",
    "y_test = np.array(y_test).reshape((y_test.shape[0],1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(X,theta):\n",
    "    z = np.exp(X @ theta.T)\n",
    "    y_hat = (z/(1+z))\n",
    "    return y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(y, y_hat):\n",
    "    cost = (-1/len(y))*np.sum((y * np.log(y_hat)) + ((1 - y) * np.log(1 - y_hat)),axis=0)\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# gradient descent algorithm\n",
    "def gradientDescent(X,y,theta,iterations,alpha, check_tol, tolerance=10**-3):\n",
    "    cost_train = []\n",
    "    cost_test = []\n",
    "    \n",
    "    for i in range(iterations):\n",
    "        theta = theta - (alpha/len(X_train)) * np.sum(X * (sigmoid(X,theta) - y), axis=0)\n",
    "        #cost[i] = costFunction(y, sigmoid(X,theta))\n",
    "        cost = costFunction(y, sigmoid(X,theta))\n",
    "        cost_train.append(cost)\n",
    "        \n",
    "        cost = costFunction(y_test, sigmoid(X_test,theta))\n",
    "        cost_test.append(cost)\n",
    "        \n",
    "        if check_tol:\n",
    "            if (i>0) and(abs((cost_train[i]-cost_train[i-1])/cost_train[i-1]) < tolerance).any():\n",
    "                print(\"Gradient Descent algorithm converged after\", i+1, \"Iterations\")\n",
    "                break\n",
    "            \n",
    "    \n",
    "    return theta,cost_train, cost_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic_regression(X, y, alpha, iterations, check_tol=False, tolerance=10**-3):\n",
    "    n = X.shape[1]\n",
    "    one_column = np.ones((X.shape[0],1))\n",
    "    X = np.concatenate((one_column, X), axis = 1)\n",
    "    theta = np.zeros((1,n+1))\n",
    "    y = np.array(y).reshape((y.shape[0],1))\n",
    "    theta, cost_train, cost_test = gradientDescent(X,y,theta,iterations,alpha,check_tol,tolerance)\n",
    "    \n",
    "    return theta,cost_train, cost_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c = logistic_regression(X_train, y_train, 0.01, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(X_test,theta):\n",
    "    return sigmoid(X_test, theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predicted = test(X_test, final_theta[0])\n",
    "\n",
    "log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "theshold_val = 0.5\n",
    "log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix :\n",
      "[[28581  7528]\n",
      " [ 8578 27793]]\n",
      "Accuracy Score : 0.7777869757174393\n",
      "Report : \n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "         0.0       0.77      0.79      0.78     36109\n",
      "         1.0       0.79      0.76      0.78     36371\n",
      "\n",
      "    accuracy                           0.78     72480\n",
      "   macro avg       0.78      0.78      0.78     72480\n",
      "weighted avg       0.78      0.78      0.78     72480\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Python script for confusion matrix creation. \n",
    "from sklearn.metrics import confusion_matrix \n",
    "from sklearn.metrics import accuracy_score \n",
    "from sklearn.metrics import classification_report \n",
    "\n",
    "results = confusion_matrix(log_df['y_actual'], log_df['y_pred']) \n",
    "print ('Confusion Matrix :')\n",
    "print(results) \n",
    "print ('Accuracy Score :',accuracy_score(log_df['y_actual'], log_df['y_pred']) )\n",
    "print ('Report : ')\n",
    "print (classification_report(log_df['y_actual'], log_df['y_pred']) )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "######---- Iteration with alpha value 0.0001 -----#####\n",
      "\n",
      "######---- Iteration with alpha value 0.001 -----#####\n",
      "\n",
      "######---- Iteration with alpha value 0.01 -----#####\n",
      "\n",
      "######---- Iteration with alpha value 0.1 -----#####\n"
     ]
    }
   ],
   "source": [
    "alpha_values = [0.0001, 0.001, 0.01, 0.1]\n",
    "\n",
    "alpha_train_theta = []\n",
    "alpha_train_cost = []\n",
    "\n",
    "alpha_test_cost = []\n",
    "\n",
    "\n",
    "for i in range(len(alpha_values)):\n",
    "    print(\"\\n######---- Iteration with alpha value\", alpha_values[i],\"-----#####\")\n",
    "    \n",
    "    theta, trainCost, testCost = logistic_regression(X_train, y_train, alpha_values[i], 10000, False)\n",
    "    \n",
    "    alpha_train_theta.append(theta)\n",
    "    alpha_train_cost.append(trainCost)\n",
    "    \n",
    "    alpha_test_cost.append(testCost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62672614])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_train_cost[0][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.62644138])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_test_cost[0][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "##### Plot for Cost vs Iterations for Each Alpha\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "\n",
    "ax1 = fig.add_subplot(2,2,1)\n",
    "\n",
    "ax1.plot(range(len(alpha_train_cost[0])),alpha_train_cost[0],'-b', label=\"Train\")\n",
    "ax1.plot(range(len(alpha_test_cost[0])),alpha_test_cost[0],'-r', label=\"Test\")\n",
    "ax1.legend(loc=\"upper right\")\n",
    "ax1.set_title(\"Cost vs Iterations for Alpha = 0.0001\")\n",
    "ax1.set_ylabel(\"Cost\")\n",
    "ax1.set_xlabel(\"Iterations\")\n",
    "ax1.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "ax1 = fig.add_subplot(2,2,2)\n",
    "\n",
    "ax1.plot(range(len(alpha_train_cost[1])),alpha_train_cost[1],'-b', label=\"Train\")\n",
    "ax1.plot(range(len(alpha_test_cost[1])),alpha_test_cost[1],'-r', label=\"Test\")\n",
    "ax1.legend(loc=\"upper right\")\n",
    "ax1.set_title(\"Cost vs Iterations for Alpha = 0.001\")\n",
    "ax1.set_ylabel(\"Cost\")\n",
    "ax1.set_xlabel(\"Iterations\")\n",
    "ax1.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax1 = fig.add_subplot(2,2,3)\n",
    "\n",
    "ax1.plot(range(len(alpha_train_cost[2])),alpha_train_cost[2],'-b', label=\"Train\")\n",
    "ax1.plot(range(len(alpha_test_cost[2])),alpha_test_cost[2],'-r', label=\"Test\")\n",
    "ax1.legend(loc=\"upper right\")\n",
    "ax1.set_title(\"Cost vs Iterations for Alpha = 0.01\")\n",
    "ax1.set_ylabel(\"Cost\")\n",
    "ax1.set_xlabel(\"Iterations\")\n",
    "ax1.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "ax1 = fig.add_subplot(2,2,4)\n",
    "\n",
    "ax1.plot(range(len(alpha_train_cost[3])),alpha_train_cost[3],'-b', label=\"Train\")\n",
    "ax1.plot(range(len(alpha_test_cost[3])),alpha_test_cost[3],'-r', label=\"Test\")\n",
    "ax1.legend(loc=\"upper right\")\n",
    "ax1.set_title(\"Cost vs Iterations for Alpha = 0.1\")\n",
    "ax1.set_ylabel(\"Cost\")\n",
    "ax1.set_xlabel(\"Iterations\")\n",
    "ax1.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#### Plots for Cost vs Iterations for Train and Test separately\n",
    "\n",
    "fig = plt.figure(figsize=(10,7))\n",
    "\n",
    "ax2 = fig.add_subplot(1,2,1)\n",
    "\n",
    "ax2.plot(range(len(alpha_train_cost[0])),alpha_train_cost[0],'-b', label=\"0.0001\")\n",
    "ax2.plot(range(len(alpha_train_cost[1])),alpha_train_cost[1],'-r', label=\"0.001\")\n",
    "ax2.plot(range(len(alpha_train_cost[2])),alpha_train_cost[2],'-g', label=\"0.01\")\n",
    "ax2.plot(range(len(alpha_train_cost[3])),alpha_train_cost[3],'-y', label=\"0.1\")\n",
    "ax2.legend(loc=\"upper right\")\n",
    "ax2.set_title(\"Cost vs Iterations for Train Set\")\n",
    "ax2.set_ylabel(\"Cost\")\n",
    "ax2.set_xlabel(\"Iterations\")\n",
    "ax2.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "\n",
    "ax2 = fig.add_subplot(1,2,2)\n",
    "\n",
    "ax2.plot(range(len(alpha_test_cost[0])),alpha_test_cost[0],'-b', label=\"0.0001\")\n",
    "ax2.plot(range(len(alpha_test_cost[1])),alpha_test_cost[1],'-r', label=\"0.001\")\n",
    "ax2.plot(range(len(alpha_test_cost[2])),alpha_test_cost[2],'-g', label=\"0.01\")\n",
    "ax2.plot(range(len(alpha_test_cost[3])),alpha_test_cost[3],'-y', label=\"0.1\")\n",
    "ax2.legend(loc=\"upper right\")\n",
    "ax2.set_title(\"Cost vs Iterations for Test Set\")\n",
    "ax2.set_ylabel(\"Cost\")\n",
    "ax2.set_xlabel(\"Iterations\")\n",
    "ax2.set_xticks(list(range(0,11000, 1000)))\n",
    "plt.xticks(rotation=90)\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_test_accuracy = []\n",
    "for i in range(len(alpha_values)):\n",
    "    y_predicted = test(X_test, alpha_train_theta[i])\n",
    "\n",
    "    log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    theshold_val = 0.5\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    alpha_test_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_train_accuracy = []\n",
    "\n",
    "one_column = np.ones((X_train.shape[0],1))\n",
    "training_set = np.concatenate((one_column, X_train), axis = 1)\n",
    "test_set = np.array(y_train).reshape((y_train.shape[0],1))\n",
    "\n",
    "for i in range(len(alpha_values)):\n",
    "    y_predicted = test(training_set, alpha_train_theta[i])\n",
    "\n",
    "    log_df = pd.DataFrame(test_set, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    theshold_val = 0.5\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    alpha_train_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha_test_error = np.ones(len(alpha_test_accuracy)) - alpha_test_accuracy\n",
    "alpha_train_error = np.ones(len(alpha_train_accuracy)) - alpha_train_accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize= (10,7))\n",
    "\n",
    "acc_plot = fig.add_subplot(1,2,1)\n",
    "\n",
    "acc_plot.plot(np.log10(alpha_values),alpha_train_accuracy,'-b', label='Train')\n",
    "acc_plot.plot(np.log10(alpha_values),alpha_test_accuracy,'-r', label='Test')\n",
    "acc_plot.legend(loc=\"upper right\")\n",
    "acc_plot.set_ylabel(\"Accuracy\")\n",
    "acc_plot.set_xlabel(\"Log(Alpha)\")\n",
    "acc_plot.set_title(\"Accuracy vs Log(Alpha)\")\n",
    "\n",
    "\n",
    "err_plot = fig.add_subplot(1,2,2)\n",
    "\n",
    "err_plot.plot(np.log10(alpha_values),alpha_train_error,'-b', label='Train')\n",
    "err_plot.plot(np.log10(alpha_values),alpha_test_error,'-r', label='Test')\n",
    "err_plot.legend(loc=\"upper right\")\n",
    "err_plot.set_ylabel(\"Error\")\n",
    "err_plot.set_xlabel(\"Log(Alpha)\")\n",
    "err_plot.set_title(\"Error vs Log(Alpha)\")\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best alpha is 0.1\n"
     ]
    }
   ],
   "source": [
    "print(\"The best alpha is 0.1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "theshold_val = [0.3,0.4,0.5,0.6,0.7]\n",
    "\n",
    "thresh_test_accuracy = []\n",
    "for i in range(len(theshold_val)):\n",
    "    y_predicted = test(X_test, alpha_train_theta[3])\n",
    "\n",
    "    log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val[i], 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val[i], 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    thresh_test_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "theshold_val = [0.3,0.4,0.5,0.6, 0.7]\n",
    "\n",
    "thresh_train_accuracy = []\n",
    "\n",
    "one_column = np.ones((X_train.shape[0],1))\n",
    "training_set = np.concatenate((one_column, X_train), axis = 1)\n",
    "test_set = np.array(y_train).reshape((y_train.shape[0],1))\n",
    "\n",
    "for i in range(len(theshold_val)):\n",
    "    y_predicted = test(training_set, alpha_train_theta[3])\n",
    "\n",
    "    log_df = pd.DataFrame(test_set, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val[i], 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val[i], 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    thresh_train_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "thresh_test_error = np.ones(len(thresh_test_accuracy)) - thresh_test_accuracy\n",
    "thresh_train_error = np.ones(len(thresh_train_accuracy)) - thresh_train_accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize= (10,7))\n",
    "\n",
    "acc_plot = fig.add_subplot(1,2,1)\n",
    "\n",
    "acc_plot.plot(theshold_val,thresh_train_accuracy,'-b', label='Train')\n",
    "acc_plot.plot(theshold_val,thresh_test_accuracy,'-r', label='Test')\n",
    "acc_plot.legend(loc=\"upper right\")\n",
    "acc_plot.set_ylabel(\"Accuracy\")\n",
    "acc_plot.set_xlabel(\"Threshold\")\n",
    "acc_plot.set_title(\"Accuracy vs Threshold\")\n",
    "\n",
    "\n",
    "err_plot = fig.add_subplot(1,2,2)\n",
    "\n",
    "err_plot.plot(theshold_val,thresh_train_error,'-b', label='Train')\n",
    "err_plot.plot(theshold_val,thresh_test_error,'-r', label='Test')\n",
    "err_plot.legend(loc=\"upper right\")\n",
    "err_plot.set_ylabel(\"Error\")\n",
    "err_plot.set_xlabel(\"Threshold\")\n",
    "err_plot.set_title(\"Error vs Threshold\")\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "######---- Iteration with alpha value 1e-07 -----#####\n",
      "Gradient Descent algorithm converged after 885 Iterations\n",
      "\n",
      "######---- Iteration with alpha value 1e-06 -----#####\n",
      "Gradient Descent algorithm converged after 655 Iterations\n",
      "\n",
      "######---- Iteration with alpha value 1e-05 -----#####\n",
      "Gradient Descent algorithm converged after 434 Iterations\n",
      "\n",
      "######---- Iteration with alpha value 0.0001 -----#####\n",
      "Gradient Descent algorithm converged after 234 Iterations\n",
      "\n",
      "######---- Iteration with alpha value 0.001 -----#####\n",
      "Gradient Descent algorithm converged after 81 Iterations\n",
      "\n",
      "######---- Iteration with alpha value 0.01 -----#####\n",
      "Gradient Descent algorithm converged after 6 Iterations\n"
     ]
    }
   ],
   "source": [
    "alpha_values = 0.1\n",
    "\n",
    "tol_val = [10**-7, 10**-6, 10**-5, 10**-4, 10**-3, 10**-2]\n",
    "\n",
    "tol_train_theta = []\n",
    "tol_train_cost = []\n",
    "\n",
    "tol_test_cost = []\n",
    "\n",
    "\n",
    "for i in range(len(tol_val)):\n",
    "    print(\"\\n######---- Iteration with tolerance value\", tol_val[i],\"-----#####\")\n",
    "    \n",
    "    theta, trainCost, testCost = logistic_regression(X_train, y_train, 0.1, 10000, True, tol_val[i])\n",
    "    \n",
    "    tol_train_theta.append(theta)\n",
    "    tol_train_cost.append(trainCost)\n",
    "    \n",
    "    tol_test_cost.append(testCost)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "tol_test_accuracy = []\n",
    "for i in range(len(tol_val)):\n",
    "    y_predicted = test(X_test, tol_train_theta[i])\n",
    "\n",
    "    log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    theshold_val = 0.5\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    tol_test_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [],
   "source": [
    "tol_train_accuracy = []\n",
    "\n",
    "one_column = np.ones((X_train.shape[0],1))\n",
    "training_set = np.concatenate((one_column, X_train), axis = 1)\n",
    "test_set = np.array(y_train).reshape((y_train.shape[0],1))\n",
    "\n",
    "for i in range(len(tol_val)):\n",
    "    y_predicted = test(training_set, tol_train_theta[i])\n",
    "\n",
    "    log_df = pd.DataFrame(test_set, columns=['y_actual']) \n",
    "    log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "    log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "    theshold_val = 0.6\n",
    "    log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "    log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "    acc = accuracy_score(log_df['y_actual'], log_df['y_pred'])\n",
    "    tol_train_accuracy.append(acc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "tol_test_error = np.ones(len(tol_test_accuracy)) - tol_test_accuracy\n",
    "tol_train_error = np.ones(len(tol_train_accuracy)) - tol_train_accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize= (10,7))\n",
    "\n",
    "acc_plot = fig.add_subplot(1,2,1)\n",
    "\n",
    "acc_plot.plot(np.log10(tol_val),tol_train_accuracy,'-b', label='Train')\n",
    "acc_plot.plot(np.log10(tol_val),tol_test_accuracy,'-r', label='Test')\n",
    "acc_plot.legend(loc=\"upper right\")\n",
    "acc_plot.set_ylabel(\"Accuracy\")\n",
    "acc_plot.set_xlabel(\"Log(Tolerance)\")\n",
    "acc_plot.set_title(\"Accuracy vs Log(Tolerance)\")\n",
    "\n",
    "\n",
    "err_plot = fig.add_subplot(1,2,2)\n",
    "\n",
    "err_plot.plot(np.log10(tol_val),tol_train_error,'-b', label='Train')\n",
    "err_plot.plot(np.log10(tol_val),tol_test_error,'-r', label='Test')\n",
    "err_plot.legend(loc=\"upper right\")\n",
    "err_plot.set_ylabel(\"Error\")\n",
    "err_plot.set_xlabel(\"Log(Tolerance)\")\n",
    "err_plot.set_title(\"Error vs Log(Tolerance)\")\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimal tolerance is 10^-4\n"
     ]
    }
   ],
   "source": [
    "print(\"The optimal tolerance is 10^-4\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "k = random.sample(range(0, 14), 8)\n",
    "\n",
    "\n",
    "# defining feature matrix(X) and response vector(y) \n",
    "X = df.iloc[:,0:8]\n",
    "y = df[\"run_class\"]\n",
    "  \n",
    "\n",
    "\n",
    "# splitting X and y into training and testing sets \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=0.3, \n",
    "                                                    random_state=1) \n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "\n",
    "X_test = scaler.fit_transform(X_test)\n",
    "one_column = np.ones((X_test.shape[0],1))\n",
    "X_test = np.concatenate((one_column, X_test), axis = 1)\n",
    "\n",
    "y_test = np.array(y_test).reshape((y_test.shape[0],1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['KWG', 'NWG', 'MDIMC', 'MDIMA', 'SA', 'KWI', 'VWN', 'NDIMC'], dtype='object')"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best alpha is 0.1\n",
      "The best tolerance value is 10^-4\n",
      "The best threshold is 0.6\n"
     ]
    }
   ],
   "source": [
    "print(\"The best alpha is 0.1\")\n",
    "print(\"The best tolerance value is 10^-4\")\n",
    "print(\"The best threshold is 0.6\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent algorithm converged after 194 Iterations\n"
     ]
    }
   ],
   "source": [
    "theta8, trainCost8, testCost8 = logistic_regression(X_train, y_train, 0.1, 10000, True, 10**-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predicted = test(X_test, theta8)\n",
    "\n",
    "log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "log_df.columns = ['y_actual', 'y_hat']\n",
    "theshold_val = 0.6\n",
    "\n",
    "log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "acc_train8 = accuracy_score(log_df['y_actual'], log_df['y_pred'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "one_column = np.ones((X_train.shape[0],1))\n",
    "training_set = np.concatenate((one_column, X_train), axis = 1)\n",
    "test_set = np.array(y_train).reshape((y_train.shape[0],1))\n",
    "\n",
    "y_predicted = test(training_set, theta8)\n",
    "\n",
    "log_df = pd.DataFrame(test_set, columns=['y_actual']) \n",
    "log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "theshold_val = 0.6\n",
    "log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "acc_test8 = accuracy_score(log_df['y_actual'], log_df['y_pred'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8224061810154525\n",
      "0.8225579470198675\n",
      "0.8186672185430464\n",
      "0.8186672185430464\n"
     ]
    }
   ],
   "source": [
    "print(acc_train8)\n",
    "print(acc_test8)\n",
    "print(tol_train_accuracy[3])\n",
    "print(tol_train_accuracy[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.00247716,  1.11118771,  0.7001912 ,  0.09228744, -0.72096318,\n",
       "        -0.60940893, -0.02931144, -0.06083945, -0.02002037,  0.01353618,\n",
       "        -0.07039227, -0.27833415, -0.02785967, -0.35018893, -0.06876217]])"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tol_train_theta[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining feature matrix(X) and response vector(y) \n",
    "k  =[0,1,3,4,9, 10,12,13]\n",
    "\n",
    "X = df.iloc[:,k]\n",
    "y = df[\"run_class\"]\n",
    "  \n",
    "\n",
    "\n",
    "# splitting X and y into training and testing sets \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=0.3, \n",
    "                                                    random_state=1) \n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "\n",
    "X_test = scaler.fit_transform(X_test)\n",
    "one_column = np.ones((X_test.shape[0],1))\n",
    "X_test = np.concatenate((one_column, X_test), axis = 1)\n",
    "\n",
    "y_test = np.array(y_test).reshape((y_test.shape[0],1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['MWG', 'NWG', 'MDIMC', 'NDIMC', 'VWN', 'STRM', 'SA', 'SB'], dtype='object')"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns[k]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Descent algorithm converged after 214 Iterations\n"
     ]
    }
   ],
   "source": [
    "theta_best, trainCost_best, testCost_best = logistic_regression(X_train, y_train, 0.1, 10000, True, 10**-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predicted = test(X_test, theta_best)\n",
    "\n",
    "log_df = pd.DataFrame(y_test, columns=['y_actual']) \n",
    "log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "log_df.columns = ['y_actual', 'y_hat']\n",
    "theshold_val = 0.6\n",
    "\n",
    "log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "acc_train_best = accuracy_score(log_df['y_actual'], log_df['y_pred'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [],
   "source": [
    "one_column = np.ones((X_train.shape[0],1))\n",
    "training_set = np.concatenate((one_column, X_train), axis = 1)\n",
    "test_set = np.array(y_train).reshape((y_train.shape[0],1))\n",
    "\n",
    "y_predicted = test(training_set, theta_best)\n",
    "\n",
    "log_df = pd.DataFrame(test_set, columns=['y_actual']) \n",
    "log_df = pd.concat([log_df, pd.DataFrame(y_predicted)], axis=1, ignore_index=True)\n",
    "log_df.columns = ['y_actual', 'y_hat']\n",
    "\n",
    "theshold_val = 0.6\n",
    "log_df.loc[log_df['y_hat'] >= theshold_val, 'y_pred'] = 1\n",
    "log_df.loc[log_df['y_hat'] < theshold_val, 'y_pred'] = 0\n",
    "\n",
    "acc_test_best = accuracy_score(log_df['y_actual'], log_df['y_pred'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8172047461368653\n",
      "0.8195364238410596\n"
     ]
    }
   ],
   "source": [
    "print(acc_train_best)\n",
    "print(acc_test_best)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression using sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score \n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "X_train = scaler.fit_transform(X_train)\n",
    "X_test = scaler.fit_transform(X_test)\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "predicted_classes = model.predict(X_test)\n",
    "accuracy = accuracy_score(y_test,predicted_classes)\n",
    "parameters = model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "accuracy"
   ]
  }
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