logistic_regression.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "logistic_regression.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4GgPS2DCsFaX",
        "outputId": "ef023bce-51e7-42c8-8ec8-23fdd8cfc9b7"
      },
      "source": [
        "# This mounts your Google Drive to the Colab VM.\n",
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "\n",
        "# TODO: Enter the foldername in your Drive where you have saved the unzipped\n",
        "# assignment folder, e.g. 'cs231n/assignments/assignment1/'\n",
        "FOLDERNAME = \"ml/logistic_regression\"\n",
        "assert FOLDERNAME is not None, \"[!] Enter the foldername.\"\n",
        "\n",
        "# Now that we've mounted your Drive, this ensures that\n",
        "# the Python interpreter of the Colab VM can load\n",
        "# python files from within it.\n",
        "import sys\n",
        "sys.path.append('/content/drive/My Drive/{}'.format(FOLDERNAME))\n",
        "\n",
        "# This downloads the CIFAR-10 dataset to your Drive\n",
        "# if it doesn't already exist.\n",
        "#%cd /content/drive/My\\ Drive/$FOLDERNAME/cs231n/datasets/\n",
        "#!bash get_datasets.sh\n",
        "#%cd /content/drive/My\\ Drive/$FOLDERNAME"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uEC0pnScTtdb"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import math"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O_VCvc39Gdxt"
      },
      "source": [
        "#Dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "A0x-AOqtJ2lY",
        "outputId": "61410361-203d-4d73-8ada-b8141e2611c0"
      },
      "source": [
        "pima = pd.read_csv(\"diabetes.csv\")\n",
        "print(pima.columns)\n",
        "columns = ['Glucose','SkinThickness','Outcome']\n",
        "df = pd.DataFrame(pima, columns=columns)\n",
        "print(df.head())"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Index(['Pregnancies', 'Glucose', 'BloodPressure', 'SkinThickness', 'Insulin',\n",
            "       'BMI', 'DiabetesPedigreeFunction', 'Age', 'Outcome'],\n",
            "      dtype='object')\n",
            "   Glucose  SkinThickness  Outcome\n",
            "0      148             35        1\n",
            "1       85             29        0\n",
            "2      183              0        1\n",
            "3       89             23        0\n",
            "4      137             35        1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NDc2R1hDj9-D"
      },
      "source": [
        "# Splitting data set into train and test \n",
        "\n",
        "dfx = df.to_numpy()\n",
        "\n",
        "train_data = dfx[0:500,:]\n",
        "test_data = dfx[500:,:]\n",
        "\n",
        "# train data \n",
        "train_X = train_data[:,0:2]\n",
        "train_y = train_data[:,2]\n",
        "\n",
        "#test data\n",
        "test_X = test_data[:,0:2]\n",
        "test_y = test_data[:,2]"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vTqhsxcPTEXa"
      },
      "source": [
        "def sigmoid(x):\n",
        "    \"\"\"A numerically stable version of the logistic sigmoid function.\"\"\"\n",
        "    pos_mask = x >= 0\n",
        "    neg_mask = x < 0\n",
        "    z = np.zeros_like(x)\n",
        "    z[pos_mask] = np.exp(-x[pos_mask])\n",
        "    z[neg_mask] = np.exp(x[neg_mask])\n",
        "    top = np.ones_like(x)\n",
        "    top[neg_mask] = z[neg_mask]\n",
        "    return top / (1 + z)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U3pAavI7jR-l"
      },
      "source": [
        "def print_every(loss,i):\n",
        "  if i%50 == 0:\n",
        "    print(\"Iteration:\",i,\"loss:\",loss)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OIbrUg3m3K_2"
      },
      "source": [
        "def normalize(x):\n",
        "  mu = np.mean(x,axis=0)\n",
        "  var = np.mean((x-mu)**2,axis=0)\n",
        "  x = (x - mu) / np.sqrt(var)\n",
        "  ones = np.ones([x.shape[0],1])\n",
        "  x = np.append(ones,x,axis=1)\n",
        "  return x,mu,var"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KhegA7KrGcDg"
      },
      "source": [
        "#Train"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gwjmYX_ZKFbH"
      },
      "source": [
        "def logistic_reg_train(x,w,y,iter,lr):\n",
        "\n",
        "  # linear function same as Linear Regression\n",
        "  n = x.shape[0]\n",
        "\n",
        "  loss_hist = []\n",
        "\n",
        "  for i in range(iter):\n",
        "\n",
        "    h = np.dot(x,w)\n",
        "    #Sigmoid Function \n",
        "    s = sigmoid(h)\n",
        "   \n",
        "    # loss function \n",
        "    loss = -(1/n) * ((np.dot(y,np.log(s))) + np.dot((1-y),np.log(1-s)))\n",
        "    print_every(loss,i)\n",
        "    \n",
        "    # Partial derivatives w.r.t w\n",
        "    \n",
        "    dw = (1/n) * np.dot((y-s),x)\n",
        "\n",
        "    #updating parameters \n",
        "    w = w + lr*dw\n",
        "\n",
        "    loss_hist.append(loss) \n",
        "\n",
        "  return w,loss_hist"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oQYYpi3HjhOl"
      },
      "source": [
        "# Normalize the inputs\n",
        "x_train_norm,mu_train,var_train = normalize(train_X)\n",
        "\n",
        "# weights initialization \n",
        "w = np.random.randn(train_X.shape[1],1) \n",
        "w = np.append(0,w)\n"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Thyn__rguUoX",
        "outputId": "57b2c7a8-0f97-4ac2-a419-66b784ce2c9a"
      },
      "source": [
        "iter = 2000\n",
        "lr = 0.003\n",
        "optim_w, loss_hist = logistic_reg_train(x_train_norm,w,train_y,iter,lr)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 0 loss: 0.670044768724279\n",
            "Iteration: 50 loss: 0.6626523557924836\n",
            "Iteration: 100 loss: 0.6556799978061332\n",
            "Iteration: 150 loss: 0.6491072494003616\n",
            "Iteration: 200 loss: 0.6429141523824431\n",
            "Iteration: 250 loss: 0.6370812981205708\n",
            "Iteration: 300 loss: 0.6315898779543568\n",
            "Iteration: 350 loss: 0.6264217225187003\n",
            "Iteration: 400 loss: 0.6215593309558392\n",
            "Iteration: 450 loss: 0.6169858910308043\n",
            "Iteration: 500 loss: 0.612685291171128\n",
            "Iteration: 550 loss: 0.6086421254300672\n",
            "Iteration: 600 loss: 0.6048416923305238\n",
            "Iteration: 650 loss: 0.6012699884901916\n",
            "Iteration: 700 loss: 0.5979136978621907\n",
            "Iteration: 750 loss: 0.594760177353653\n",
            "Iteration: 800 loss: 0.5917974395106935\n",
            "Iteration: 850 loss: 0.5890141328844253\n",
            "Iteration: 900 loss: 0.5863995206210857\n",
            "Iteration: 950 loss: 0.5839434577512648\n",
            "Iteration: 1000 loss: 0.5816363675895684\n",
            "Iteration: 1050 loss: 0.5794692175973817\n",
            "Iteration: 1100 loss: 0.5774334950079463\n",
            "Iteration: 1150 loss: 0.5755211824648213\n",
            "Iteration: 1200 loss: 0.5737247338818299\n",
            "Iteration: 1250 loss: 0.5720370506945847\n",
            "Iteration: 1300 loss: 0.5704514586403434\n",
            "Iteration: 1350 loss: 0.5689616851739256\n",
            "Iteration: 1400 loss: 0.5675618376023547\n",
            "Iteration: 1450 loss: 0.5662463819993975\n",
            "Iteration: 1500 loss: 0.565010122942904\n",
            "Iteration: 1550 loss: 0.5638481841024198\n",
            "Iteration: 1600 loss: 0.5627559896916551\n",
            "Iteration: 1650 loss: 0.5617292467897003\n",
            "Iteration: 1700 loss: 0.5607639285261273\n",
            "Iteration: 1750 loss: 0.5598562581180195\n",
            "Iteration: 1800 loss: 0.5590026937413304\n",
            "Iteration: 1850 loss: 0.5581999142145451\n",
            "Iteration: 1900 loss: 0.5574448054692442\n",
            "Iteration: 1950 loss: 0.5567344477796855\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bD_jQkYq_5AB"
      },
      "source": [
        "## Predict"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JQBVIF062daS"
      },
      "source": [
        "def predict(x,y,w):\n",
        "\n",
        "  h = np.dot(x,w)\n",
        "  s = sigmoid(h)\n",
        "  y_pred = []\n",
        "  for i in range(len(s)):\n",
        "    if s[i] >= 0.5:\n",
        "      y_pred.append(1)\n",
        "    else:\n",
        "      y_pred.append(0)\n",
        "  \n",
        "  return y_pred"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mjGgYuBT3Ilb",
        "outputId": "23e17d51-16f9-4827-b1f1-d7ee781a0621"
      },
      "source": [
        "x_test_norm,mu,var = normalize(test_X)\n",
        "\n",
        "pred_y = predict(x_test_norm,test_y,optim_w)\n",
        "pred_y = np.array(pred_y)\n",
        "\n",
        "#Calculating the accuracy \n",
        "count = 0\n",
        "for i in range(len(test_y)):\n",
        "  if test_y[i]==pred_y[i]:\n",
        "    count+=1\n",
        "\n",
        "print(\"Prediction Accuracy:\",(count/len(test_y)*100))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prediction Accuracy: 77.61194029850746\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2zPx6Kz__zLQ"
      },
      "source": [
        "# Plotting the decision boundary "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        },
        "id": "bkiPAH_Bu3hJ",
        "outputId": "9efa9ccb-33a1-4747-ed71-3e41df304905"
      },
      "source": [
        "# we will try to plot with different colors \n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sbn\n",
        "plt.figure(figsize=(8, 8), dpi=80)\n",
        "sbn.scatterplot(x=test_X[:, 0][test_y==0], y=test_X[:, 1][test_y==0],color='green')\n",
        "sbn.scatterplot(x=test_X[:, 0][test_y==1], y=test_X[:, 1][test_y==1],color='blue')\n",
        "\n",
        "#plt.margins(x=-0.25, y=-0.25)\n",
        "decision_boundary =  (-(optim_w[0] + (optim_w[1]) *x_train_norm[:,1])) /(optim_w[2]/10)\n",
        "plt.plot(train_X[:,0],decision_boundary,color='red')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x640 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TXXeFOL_AMU-"
      },
      "source": [
        "Try out different set of data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "73w_goIUAVC9",
        "outputId": "7fc6ffc9-dd49-4238-c07a-00aa1fe3cf96"
      },
      "source": [
        "pima = pd.read_csv(\"diabetes.csv\")\n",
        "print(pima.columns)\n",
        "columns = ['Glucose','Age','Outcome']\n",
        "df = pd.DataFrame(pima, columns=columns)\n",
        "print(df.head())"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Index(['Pregnancies', 'Glucose', 'BloodPressure', 'SkinThickness', 'Insulin',\n",
            "       'BMI', 'DiabetesPedigreeFunction', 'Age', 'Outcome'],\n",
            "      dtype='object')\n",
            "   Glucose  Age  Outcome\n",
            "0      148   50        1\n",
            "1       85   31        0\n",
            "2      183   32        1\n",
            "3       89   21        0\n",
            "4      137   33        1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bU17YW18AVJr"
      },
      "source": [
        "# Splitting data set into train and test \n",
        "\n",
        "dfx = df.to_numpy()\n",
        "\n",
        "train_data = dfx[0:500,:]\n",
        "test_data = dfx[500:,:]\n",
        "\n",
        "# train data \n",
        "train_X = train_data[:,0:2]\n",
        "train_y = train_data[:,2]\n",
        "\n",
        "#test data\n",
        "test_X = test_data[:,0:2]\n",
        "test_y = test_data[:,2]"
      ],
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BazPrEzSAVNz"
      },
      "source": [
        "# Normalize the inputs\n",
        "x_train_norm,mu_train,var_train = normalize(train_X)\n",
        "\n",
        "# weights initialization \n",
        "w = np.random.randn(train_X.shape[1],1) \n",
        "w = np.append(0,w)\n"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wiVTOU5qAVRw",
        "outputId": "2c3e1cb1-213b-4e4b-be12-770d142a7975"
      },
      "source": [
        "iter = 2000\n",
        "lr = 0.003\n",
        "optim_w, loss_hist = logistic_reg_train(x_train_norm,w,train_y,iter,lr)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Iteration: 0 loss: 0.6536393076313141\n",
            "Iteration: 50 loss: 0.6492563106039907\n",
            "Iteration: 100 loss: 0.6450014258419662\n",
            "Iteration: 150 loss: 0.6408730876433092\n",
            "Iteration: 200 loss: 0.6368696791982097\n",
            "Iteration: 250 loss: 0.632989532059511\n",
            "Iteration: 300 loss: 0.629230925912058\n",
            "Iteration: 350 loss: 0.6255920886469993\n",
            "Iteration: 400 loss: 0.6220711967451137\n",
            "Iteration: 450 loss: 0.61866637597101\n",
            "Iteration: 500 loss: 0.6153757023777348\n",
            "Iteration: 550 loss: 0.6121972036189006\n",
            "Iteration: 600 loss: 0.6091288605629931\n",
            "Iteration: 650 loss: 0.6061686092020252\n",
            "Iteration: 700 loss: 0.603314342844242\n",
            "Iteration: 750 loss: 0.6005639145781453\n",
            "Iteration: 800 loss: 0.5979151399927768\n",
            "Iteration: 850 loss: 0.5953658001369553\n",
            "Iteration: 900 loss: 0.5929136446980983\n",
            "Iteration: 950 loss: 0.5905563953793473\n",
            "Iteration: 1000 loss: 0.5882917494520337\n",
            "Iteration: 1050 loss: 0.5861173834590634\n",
            "Iteration: 1100 loss: 0.5840309570436123\n",
            "Iteration: 1150 loss: 0.582030116876602\n",
            "Iteration: 1200 loss: 0.580112500655817\n",
            "Iteration: 1250 loss: 0.5782757411492054\n",
            "Iteration: 1300 loss: 0.5765174702549023\n",
            "Iteration: 1350 loss: 0.574835323050825\n",
            "Iteration: 1400 loss: 0.5732269418072925\n",
            "Iteration: 1450 loss: 0.5716899799370264\n",
            "Iteration: 1500 loss: 0.5702221058580564\n",
            "Iteration: 1550 loss: 0.5688210067464866\n",
            "Iteration: 1600 loss: 0.5674843921577114\n",
            "Iteration: 1650 loss: 0.5662099974965321\n",
            "Iteration: 1700 loss: 0.5649955873186046\n",
            "Iteration: 1750 loss: 0.5638389584477951\n",
            "Iteration: 1800 loss: 0.5627379428962258\n",
            "Iteration: 1850 loss: 0.5616904105760655\n",
            "Iteration: 1900 loss: 0.560694271794407\n",
            "Iteration: 1950 loss: 0.5597474795248379\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nFIoeSzPAjJ2"
      },
      "source": [
        "##Predict"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7jyPE4EfAVUd",
        "outputId": "6f00454d-1200-4747-a436-fa7648c669ca"
      },
      "source": [
        "x_test_norm,mu,var = normalize(test_X)\n",
        "\n",
        "pred_y = predict(x_test_norm,test_y,optim_w)\n",
        "pred_y = np.array(pred_y)\n",
        "\n",
        "#Calculating the accuracy \n",
        "count = 0\n",
        "for i in range(len(test_y)):\n",
        "  if test_y[i]==pred_y[i]:\n",
        "    count+=1\n",
        "\n",
        "print(\"Prediction Accuracy:\",(count/len(test_y)*100))"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prediction Accuracy: 79.8507462686567\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        },
        "id": "CN7b0McYA5d0",
        "outputId": "7921ec42-3dfd-4e63-8331-34aad6ece9d2"
      },
      "source": [
        "# we will try to plot with different colors \n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sbn\n",
        "\n",
        "plt.figure(figsize=(8, 8), dpi=80)\n",
        "decision_boundary = (-(optim_w[0] + (optim_w[1]) *x_train_norm[:,1])) /(optim_w[2]/10)\n",
        "plt.plot(train_X[:,0],decision_boundary,color='blue')\n",
        "sbn.scatterplot(x=test_X[:, 0][test_y==0],y= test_X[:, 1][test_y==0],color='green')\n",
        "sbn.scatterplot(x=test_X[:, 0][test_y==1],y= test_X[:, 1][test_y==1],color='orange')\n",
        "\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x640 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}