Implementing SGD Classifier with Logloss and L2 Regularization from scratch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7eiDWcM_MC3H"
   },
   "source": [
    "# <font color='red'>Implement SGD Classifier with Logloss and L2 regularization Using SGD without using sklearn</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Fk5DSPCLxqT-"
   },
   "source": [
    "<font color='red'> Importing packages</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "42Et8BKIxnsp"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.datasets import make_classification\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn import linear_model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NpSk3WQBx7TQ"
   },
   "source": [
    "<font color='red'>Creating custom dataset</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "BsMp0oWzx6dv"
   },
   "outputs": [],
   "source": [
    "X, y = make_classification(n_samples=50000, n_features=15, n_informative=10, n_redundant=5,\n",
    "                           n_classes=2, weights=[0.7], class_sep=0.7, random_state=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "L8W2fg1cyGdX",
    "outputId": "40e5e725-5c8d-403a-b702-162682502424"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((50000, 15), (50000,))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x99RWCgpqNHw"
   },
   "source": [
    "<font color='red'>Splitting data into train and test </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "id": "0Kh4dBfVyJMP"
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "0DR_YMBsyOci",
    "outputId": "09f82cd3-ca4e-49d9-c292-411fa848b74d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((37500, 15), (37500,), (12500, 15), (12500,))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape, y_train.shape, X_test.shape, y_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_-CcGTKgsMrY"
   },
   "source": [
    "\n",
    "\n",
    "\n",
    "## <font color='red' size=5> Implementing Logistic Regression with L2 regularization Using SGD: without using sklearn </font>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zU2Y3-FQuJ3z"
   },
   "source": [
    "\n",
    "<br>\n",
    "Algorithm\n",
    "\n",
    "* Initialize the weight_vector and intercept term to zeros </font>\n",
    "\n",
    "* Create a loss function \n",
    "\n",
    " $log loss = -1*\\frac{1}{n}\\Sigma_{for each Yt,Y_{pred}}(Ytlog10(Y_{pred})+(1-Yt)log10(1-Y_{pred}))$\n",
    "- for each epoch:\n",
    "\n",
    "    - for each batch of data points in train: (keeping batch size=1)\n",
    "\n",
    "        - calculate the gradient of loss function w.r.t each weight in weight vector\n",
    "        $dw^{(t)} = x_n(y_n − σ((w^{(t)})^{T} x_n+b^{t}))- \\frac{λ}{N}w^{(t)})$ <br>\n",
    "\n",
    "        - Calculate the gradient of the intercept <a href='https://drive.google.com/file/d/1nQ08-XY4zvOLzRX-lGf8EYB5arb7-m1H/view?usp=sharing'>check this</a>\n",
    "\n",
    "           $ db^{(t)} = y_n- σ((w^{(t)})^{T} x_n+b^{t}))$\n",
    "\n",
    "        - Update weights and intercept (check the equation number 32 in the above mentioned <a href='https://drive.google.com/file/d/1nQ08-XY4zvOLzRX-lGf8EYB5arb7-m1H/view?usp=sharing'>pdf</a>): <br>\n",
    "        $w^{(t+1)}← w^{(t)}+α(dw^{(t)}) $<br>\n",
    "\n",
    "        $b^{(t+1)}←b^{(t)}+α(db^{(t)}) $\n",
    "    - calculate the log loss for train and test with the updated weights \n",
    "    - And if you wish, you can compare the previous loss and the current loss, if it is not updating, then\n",
    "        you can stop the training\n",
    "    - append this loss in the list ( this will be used to see how loss is changing for each epoch after the training is over )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZR_HgjgS_wKu"
   },
   "source": [
    "<font color='blue'>Initializing weights </font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "GecwYV9fsKZ9"
   },
   "outputs": [],
   "source": [
    "from numpy import zeros_like\n",
    "def initialize_weights(row_vector):\n",
    "    ''' initializing our weights and bias'''\n",
    "    w=zeros_like(row_vector)\n",
    "    b=0\n",
    "    return w,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "QlaVSAw2EiH1",
    "outputId": "38b03a86-62c6-42e1-beed-a1d38c4aef47"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]), 0)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initialize_weights(X[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "uPWTdxPgD3Ux",
    "outputId": "93ce08e9-414d-4931-c18b-85316858f9dc"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(15,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "A7I6uWBRsKc4",
    "outputId": "97cd5afc-d9c8-44a9-ad5d-64a2a20a579a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      "b = 0\n"
     ]
    }
   ],
   "source": [
    "dim=X_train[0] \n",
    "w,b = initialize_weights(X[0])\n",
    "print('w =',(w))\n",
    "print('b =',str(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QN83oMWy_5rv"
   },
   "source": [
    "<font color='blue'>Computing sigmoid </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qPv4NJuxABgs"
   },
   "source": [
    "$sigmoid(z)= 1/(1+exp(-z))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "nAfmQF47_Sd6"
   },
   "outputs": [],
   "source": [
    "from math import *\n",
    "def sigmoid(z):\n",
    "    ''' In this function, we will return sigmoid of z'''\n",
    "    # compute sigmoid(z) and returnz\n",
    "    return 1/(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gS7JXbcrBOFF"
   },
   "source": [
    "<font color='blue'> Computing loss </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lfEiS22zBVYy"
   },
   "source": [
    "$log loss = -1*\\frac{1}{n}\\Sigma_{for each Yt,Y_{pred}}(Ytlog10(Y_{pred})+(1-Yt)log10(1-Y_{pred}))$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "id": "VaFDgsp3sKi6"
   },
   "outputs": [],
   "source": [
    "def logloss(y_true,y_pred):\n",
    "    loss=-1*np.mean(y_true*np.log10(y_pred)+(1-y_true)*np.log10(1-y_pred))\n",
    "    return loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tQabIadLCBAB"
   },
   "source": [
    "<font color='blue'>Computing gradient w.r.to  'w' </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "YTMxiYKaCQgd"
   },
   "source": [
    "$dw^{(t)} = x_n(y_n − σ((w^{(t)})^{T} x_n+b^{t}))- \\frac{λ}{N}w^{(t)}$ <br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "id": "NMVikyuFsKo5"
   },
   "outputs": [],
   "source": [
    "def gradient_dw(x,y,w,b,alpha,N):\n",
    "    '''In this function, we will compute the gardient w.r.to w '''\n",
    "    dw=x*(y-sigmoid(np.dot(w,x)+b))-(alpha/N)*w\n",
    "    return dw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LE8g84_GI62n"
   },
   "source": [
    "<font color='blue'>Computing gradient w.r.to 'b' </font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fHvTYZzZJJ_N"
   },
   "source": [
    "$ db^{(t)} = y_n- σ((w^{(t)})^{T} x_n+b^{t})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_db(x,y,w,b):\n",
    "     '''In this function, we will compute gradient w.r.to b '''\n",
    "     db=y-sigmoid(np.dot(w,x)+b)\n",
    "     return db"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "id": "MJOSP3L88epv"
   },
   "outputs": [],
   "source": [
    "# prediction function used to compute predicted_y given the dataset X\n",
    "def pred(w,b, X):\n",
    "    N = len(X)\n",
    "    predict = []\n",
    "    for i in range(N):\n",
    "        z=np.dot(w,X[i])+b\n",
    "        predict.append(sigmoid(z))\n",
    "    return np.array(predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "id": "VKHPqAbzjWI7"
   },
   "outputs": [],
   "source": [
    "from tqdm.notebook import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TCK0jY_EOvyU"
   },
   "source": [
    "<font color='blue'> Implementing logistic regression</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "id": "dmAdc5ejEZ25"
   },
   "outputs": [],
   "source": [
    "def train(X_train,y_train,X_test,y_test,epochs,alpha,eta0):\n",
    "    ''' implementing logistic regression from scratch'''\n",
    "    train_loss = []\n",
    "    test_loss = []\n",
    "    w,b = initialize_weights(X_train[0]) # Initialize the weights\n",
    "    #write your code to perform SGD\n",
    "    for i in tqdm(range(epochs)):\n",
    "      for k,j in zip(X_train,y_train):\n",
    "        dw=gradient_dw(k,j,w,b,alpha,1)\n",
    "        db=gradient_db(k,j,w,b)\n",
    "        w=w+eta0*dw\n",
    "        b=b+eta0*db\n",
    "      #print(w,b)\n",
    "      #print(dw,db)\n",
    "      predicted_train=pred(w,b,X_train)\n",
    "      train_loss.append(logloss(y_train,predicted_train))\n",
    "      predicted_test=pred(w,b,X_test)\n",
    "      #print(predicted_test,y_test)\n",
    "      test_loss.append(logloss(y_test,predicted_test))\n",
    "      print(\"epochs {}\".format(i))\n",
    "      print(\"train loss {}\".format(train_loss[i]))\n",
    "      print(\"test loss {}\".format(test_loss[i]))\n",
    "    return w,b,train_loss,test_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
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    "id": "sUquz7LFEZ6E",
    "outputId": "f38be78f-de06-4b10-f5db-96a01ca0a333"
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   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "08b8f9702dc142dcaba4dedbec4e4c69",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/10 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epochs 0\n",
      "train loss 0.16508582909709507\n",
      "test loss 0.16616609041599303\n",
      "epochs 1\n",
      "train loss 0.16506219715226675\n",
      "test loss 0.16613687944022942\n",
      "epochs 2\n",
      "train loss 0.1650626204724662\n",
      "test loss 0.1661369826890975\n",
      "epochs 3\n",
      "train loss 0.1650626532171315\n",
      "test loss 0.1661369961684692\n",
      "epochs 4\n",
      "train loss 0.165062655254186\n",
      "test loss 0.16613699702404586\n",
      "epochs 5\n",
      "train loss 0.16506265537944248\n",
      "test loss 0.16613699707671928\n",
      "epochs 6\n",
      "train loss 0.16506265538713893\n",
      "test loss 0.16613699707995605\n",
      "epochs 7\n",
      "train loss 0.1650626553876119\n",
      "test loss 0.16613699708015497\n",
      "epochs 8\n",
      "train loss 0.16506265538764092\n",
      "test loss 0.16613699708016713\n",
      "epochs 9\n",
      "train loss 0.1650626553876427\n",
      "test loss 0.16613699708016788\n"
     ]
    }
   ],
   "source": [
    "alpha=0.001\n",
    "eta0=0.001\n",
    "N=len(X_train)\n",
    "epochs=10\n",
    "w,b,train_loss,test_loss=train(X_train,y_train,X_test,y_test,epochs,alpha,eta0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "qV1x9zoJ8epw",
    "outputId": "15d5711c-547d-4415-d962-fc868e7bdfa5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.41143756  0.1913536  -0.14834881  0.32432742 -0.22295579  0.58274586\n",
      " -0.42548225 -0.09976555  0.21372059  0.15398406  0.17752567 -0.01315215\n",
      " -0.06438781  0.36130797 -0.00957985]\n",
      "-0.9000008692366803\n"
     ]
    }
   ],
   "source": [
    "#value of weights w and bias b\n",
    "print(w)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "230YbSgNSUrQ"
   },
   "source": [
    "<font color='blue'>Ploting train and test loss vs epochs </font>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "id": "1O6GrRt7UeCJ"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 301
    },
    "id": "FUN8puFoEZtU",
    "outputId": "96534f23-ae21-4d33-e067-0425f9f67fd0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'loss')"
      ]
     },
     "execution_count": 21,
     "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": [
    "plt.plot(list(range(epochs)),test_loss,label='test loss')\n",
    "plt.plot(list(range(epochs)),train_loss,label='train loss')\n",
    "plt.legend()\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(0,0.2)\n",
    "plt.xlabel('epoch')\n",
    "plt.ylabel('loss')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
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