ML_Lab3_scratch.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ML_Lab3_scratch.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyNYKwKebmiXlE9Bx/U5Jqc3",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/JARACH-209/AI-ML_Lab/blob/master/ML_Lab3_scratch.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "syLNZFb_Nnc0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "10bd95eb-de3e-4423-b779-4a93fa5e36f8"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn import preprocessing\n",
        "from sklearn.metrics import mean_absolute_error\n",
        "from sklearn.metrics import r2_score\n",
        "from numpy.random import sample\n",
        "%matplotlib inline\n",
        "\n",
        "df = pd.read_excel(\"/content/insurance_dataset.xls\")"
      ],
      "execution_count": 206,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "*** No CODEPAGE record, no encoding_override: will use 'ascii'\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uoUWd_PZUX5w",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Train and Test set split into 80% and 20% respectively\n",
        "x_train, x_rest, y_train, y_rest = train_test_split(df.X,df.Y,test_size = .4,random_state =0)\n",
        "#Rest of the 40% set split into equal parts of Train and Validation set \n",
        "x_test, x_val, y_test, y_val = train_test_split(x_train,y_train,test_size = .5,random_state = 0)\n",
        "#Therefore : Train = 60%, Test = 20% and Validation = 20%"
      ],
      "execution_count": 207,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4RY3Bt3zTfmn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "e029bce0-9436-46a5-cd31-edbbe564da6f"
      },
      "source": [
        "x_mean = np.mean(x_train)\n",
        "y_mean = np.mean(y_train)\n",
        "n = len(x_train)# using the formula to calculate the b1 and b0\n",
        "numerator = 0\n",
        "denominator = 0\n",
        "X = np.array(x_train)\n",
        "Y = np.array(y_train)\n",
        "for i in range(n):\n",
        "    numerator += (X[i] - x_mean) * (Y[i] - y_mean)\n",
        "    denominator += (X[i] - x_mean) ** 2\n",
        "    \n",
        "b1 = numerator / denominator\n",
        "b0 = y_mean - (b1 * x_mean)\n",
        "C = b0\n",
        "M = b1\n",
        "print(b1, b0)"
      ],
      "execution_count": 208,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "3.416948742599191 18.31114211789668\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IjHBujZfUpaw",
        "colab_type": "text"
      },
      "source": [
        "intercept and slope on whole set : \n",
        "3.4138235600663664 19.99448575911481"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ojOk2MRvVdoL",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def pred_y(x):\n",
        "    return (C + M * x)\n",
        "    \n",
        "def predict(x):\n",
        "    y_pred = []\n",
        "    for value in x:\n",
        "        y_pred.append(pred_y(value))\n",
        "    return y_pred"
      ],
      "execution_count": 209,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ch3npxcUV_ez",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "outputId": "1aa3482a-b591-4b6c-bf69-6905cb47318c"
      },
      "source": [
        "plt.scatter(x_train,y_train)\n",
        "plt.plot(x_train,predict(x_train),color = \"red\")    #best fit line"
      ],
      "execution_count": 210,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd9a31fcc88>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 210
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l32_A23fXZBn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "20699d71-6c19-498a-9957-a94e784fb875"
      },
      "source": [
        "print(\"Mean Absolute Error on Test:  %.3f\" % mean_absolute_error(y_test,predict(x_test)))\n",
        "print(\"Mean Absolute Error on Train: %.3f\" %mean_absolute_error(y_train,predict(x_train)))"
      ],
      "execution_count": 211,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean Absolute Error on Test:  30.821\n",
            "Mean Absolute Error on Train: 29.748\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vQJy5BVMvlg5",
        "colab_type": "text"
      },
      "source": [
        "Using Gradient descent\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tbL5UDwj1QWX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "x_train = np.array(x_train)\n",
        "x_test = np.array(x_test)\n",
        "y_train = np.array(x_train)\n",
        "y_test = np.array(x_test)\n",
        "x_train = x_train.reshape(-1,1)\n",
        "y_train = y_train.reshape(-1,1)\n",
        "x_test = x_test.reshape(-1,1)\n",
        "y_test = y_test.reshape(-1,1)"
      ],
      "execution_count": 212,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DmysybYZ0__G",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "scaler = preprocessing.StandardScaler().fit(x_train)\n",
        "x_train = scaler.transform(x_train)\n",
        "x_test=scaler.transform(x_test)"
      ],
      "execution_count": 213,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xzmwA_muvodp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def gradientDescent(x,y,lr, epochs):\n",
        "    costs = []\n",
        "    b0, b1 = 0.0, 1.0\n",
        "    for epoch in range(epochs):\n",
        "        # initialize to 0 -> cost of epoch, Jb_0, Jb_1\n",
        "        epoch_cost, cost_b0, cost_b1 = 0, 0, 0\n",
        "        \n",
        "        for i in range(len(x)):\n",
        "            # make prediction\n",
        "            y_pred = (b0 + b1*x[i])\n",
        "            # append squared error\n",
        "            epoch_cost += (y[i] - y_pred)**2 \n",
        "            \n",
        "            for j in range(len(x)):\n",
        "                # partial derivative of b0 and b1 for current row\n",
        "                partial_wrt_b0 = -2 * (y[j] - (b0 + b1*x[j]))\n",
        "                partial_wrt_b1 = (-2 * x[j]) * (y[j] - (b0 + b1*x[j]))\n",
        "                \n",
        "                # increase cost of coeffs\n",
        "                cost_b0 += partial_wrt_b0\n",
        "                cost_b1 += partial_wrt_b1\n",
        "\n",
        "            # calculate new coeffs\n",
        "            b0 = b0 - lr * cost_b0\n",
        "            b1 = b1 - lr * cost_b1\n",
        "            \n",
        "        # keep track of errors - for visualization purposes\n",
        "        costs.append(epoch_cost)\n",
        "    return b0,b1,costs\n"
      ],
      "execution_count": 214,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hOIdvIY9yvLK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "C,M,costs = gradientDescent(x_train,y_train,0.001,15)"
      ],
      "execution_count": 215,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8RXhEJ087fdA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predict(x,C,M):\n",
        "    y_pred = []\n",
        "    for value in x:\n",
        "        y = (C + M * value)\n",
        "        y_pred.append(y)\n",
        "    return y_pred"
      ],
      "execution_count": 216,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VWHlr0Hx7sJG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "outputId": "a8114be5-c87a-47eb-fdd6-e7a6390f587c"
      },
      "source": [
        "plt.plot(range(1,len(costs)+1),costs)"
      ],
      "execution_count": 217,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd9a31227b8>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 217
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kBmZxXMP8xTN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_pred = predict(x_test,C,M)"
      ],
      "execution_count": 218,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R0RC6YG-86rL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "a89b7f54-82c5-464f-a997-c7ba72a8ab6a"
      },
      "source": [
        "print(\"Mean Absolute Error on Test:  %.3f\" %mean_absolute_error(y_test.reshape(-1,1),y_pred))\n",
        "print(\"Mean Absolute Error on Train: %.3f\" %mean_absolute_error(y_train,predict(x_train,C,M)))"
      ],
      "execution_count": 219,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean Absolute Error on Test:  0.080\n",
            "Mean Absolute Error on Train: 0.117\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k5AEq77R--bz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 36
        },
        "outputId": "225f839f-60f1-43ce-e8ee-61e6a0d2b166"
      },
      "source": [
        "print(r2_score(y_train,predict(x_train,C,M)))"
      ],
      "execution_count": 220,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.9999624052841763\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5QWWCvFA-Pj6",
        "colab_type": "text"
      },
      "source": [
        "Part 2 : Boston Housing "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rAg9ReBk-PKb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "outputId": "002c7980-d63e-46e3-fc03-c38061ed35d6"
      },
      "source": [
        "from sklearn.datasets import load_boston\n",
        "\n",
        "boston_df = pd.DataFrame(load_boston().data,columns = load_boston().feature_names)\n",
        "\n",
        "y = load_boston().target\n",
        "x = load_boston().data\n",
        "\n",
        "boston_df.head(5)"
      ],
      "execution_count": 221,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      CRIM    ZN  INDUS  CHAS    NOX  ...  RAD    TAX  PTRATIO       B  LSTAT\n",
              "0  0.00632  18.0   2.31   0.0  0.538  ...  1.0  296.0     15.3  396.90   4.98\n",
              "1  0.02731   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  396.90   9.14\n",
              "2  0.02729   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  392.83   4.03\n",
              "3  0.03237   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  394.63   2.94\n",
              "4  0.06905   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  396.90   5.33\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 221
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dubNC3RF_psq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Train and Test set split into 80% and 20% respectively\n",
        "x_train, x_rest, y_train, y_rest = train_test_split(x,y,test_size = .4,random_state =0)\n",
        "\n",
        "#Rest of the 40% set split into equal parts of Train and Validation set \n",
        "x_test, x_val, y_test, y_val = train_test_split(x_train,y_train,test_size = .5,random_state = 0)\n",
        "\n",
        "#Therefore : Train = 60%, Test = 20% and Validation = 20%"
      ],
      "execution_count": 222,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4jmitQm2_zsB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "scaler = preprocessing.StandardScaler().fit(x_train)\n",
        "x_train = scaler.transform(x_train)\n",
        "x_test = scaler.transform(x_test)\n",
        "x_val = scaler.transform(x_val)\n",
        "\n",
        "y_train = y_train.reshape(-1)\n",
        "y_test = y_test.reshape(-1)\n",
        "y_val = y_val.reshape(-1)"
      ],
      "execution_count": 223,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1fG1nr55DT9t",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def multiGrad(train_data,learning_rate,n_iter,k):\n",
        "    \n",
        "    # Initially we will keep our W and B as 0 as per the Training Data\n",
        "    w=np.zeros(shape=(1,train_data.shape[1]-1))\n",
        "    b=0\n",
        "    \n",
        "    cur_iter=1\n",
        "    while(cur_iter<=n_iter): \n",
        "\n",
        "        # create a small training data set of size K (Batches of size K)\n",
        "        temp=train_data.sample(k)\n",
        "        \n",
        "        # X and Y from the above temp dataset\n",
        "        y=np.array(temp[13])\n",
        "        x=np.array(temp.drop(13,axis=1))\n",
        "        \n",
        "        # initial gradients as 0\n",
        "        w_gradient=np.zeros(shape=(1,train_data.shape[1]-1))\n",
        "        b_gradient=0\n",
        "        \n",
        "        for i in range(k): # Calculating gradients for point in our dataset\n",
        "            prediction=np.dot(w,x[i])+b\n",
        "            w_gradient=w_gradient+(-2)*x[i]*(y[i]-(prediction))\n",
        "            b_gradient=b_gradient+(-2)*(y[i]-(prediction))\n",
        "        \n",
        "        #Updating the weights(W) and Bias(b) with the above calculated Gradients\n",
        "        w=w-learning_rate*(w_gradient/k)\n",
        "        b=b-learning_rate*(b_gradient/k)\n",
        "        \n",
        "        cur_iter=cur_iter+1\n",
        "    return w,b #Returning the weights and Bias"
      ],
      "execution_count": 224,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ihno354tG_y1",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def predict(x,w,b):\n",
        "    y_pred=[]\n",
        "    for i in range(len(x)):\n",
        "        y=np.asscalar(np.dot(w,x[i])+b)\n",
        "        y_pred.append(y)\n",
        "    return np.array(y_pred)"
      ],
      "execution_count": 225,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1ZwcHLbcENu9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "train_data = pd.DataFrame(x_train)\n",
        "train_data[13] = y_train"
      ],
      "execution_count": 226,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SXWUTvcf_53_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "w,b = multiGrad(train_data,0.001,1000,10)   #using our Gradient Descent regressor"
      ],
      "execution_count": 227,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pjPUqza-GwjR",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "y_pred = predict(x_test,w,b)\n",
        "y_pred_train = predict(x_train,w,b)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CQ-Ymd9RHxBo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "bd44d863-a17d-43e2-b290-7d15d62caf0c"
      },
      "source": [
        "print(\"Mean Absolute Error on Test:  %.3f\" % mean_absolute_error(y_test,y_pred))\n",
        "print(\"Mean Absolute Error on Train: %.3f\" %mean_absolute_error(y_train,y_pred_train))"
      ],
      "execution_count": 274,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean Absolute Error on Test:  3.685\n",
            "Mean Absolute Error on Train: 3.770\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}