sgd_on_boston_dataset.ipynb

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  "metadata": {
    "colab": {
      "name": "Implement_SGD_FINAL.ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "SNWzIHzv2ppL",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## IMPLEMENTING SGD FROM SCATCH AND COMPARING IT WITH SGD REGRESSOR"
      ]
    },
    {
      "metadata": {
        "id": "REYPoTJ1Af7u",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "from sklearn.datasets import load_boston\n",
        "from random import seed\n",
        "from random import randrange\n",
        "from csv import reader\n",
        "from math import sqrt\n",
        "from sklearn import preprocessing\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.linear_model import SGDRegressor\n",
        "from sklearn import preprocessing\n",
        "from sklearn.metrics import mean_squared_error"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "5-PxSZMG3HGw",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##LOADING THE BOSTON DATASET WHICH IS READILY AVAIABLE IN GOOGLE COLAB ADN IMPLEMENTING MODEL ON TOP OF IT"
      ]
    },
    {
      "metadata": {
        "id": "NTQ2iH-kAwbo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "X = load_boston().data\n",
        "Y = load_boston().target"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "NbPyR4kztfUH",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_boston\n",
        "boston = load_boston()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "J6qlB3C6tg_p",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "3a7bcb87-9c28-40c1-f1a5-6ce523b23c8e"
      },
      "cell_type": "code",
      "source": [
        "print(boston.feature_names)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO'\n",
            " 'B' 'LSTAT']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "_YbuFfVT3Udp",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## USING STANDARD SCALER STANDARDISING THE DATA OF THE X"
      ]
    },
    {
      "metadata": {
        "id": "FgUW39s6Be0U",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "scaler = preprocessing.StandardScaler().fit(X)\n",
        "X = scaler.transform(X)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "HNu1sXtEBBS2",
        "colab_type": "code",
        "outputId": "249adbdb-a527-4fbd-94a8-ec5f3c98e8b3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "cell_type": "code",
      "source": [
        "clf = SGDRegressor(n_iter=1000)\n",
        "clf.fit(X, Y)\n",
        "print(mean_squared_error(Y, clf.predict(X)))"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "23.059860379742734\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "llxLZ9aC9JIC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "9b06865e-7257-496a-961c-8067514e6c6d"
      },
      "cell_type": "code",
      "source": [
        "clf"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDRegressor(alpha=0.0001, average=False, early_stopping=False, epsilon=0.1,\n",
              "       eta0=0.01, fit_intercept=True, l1_ratio=0.15,\n",
              "       learning_rate='invscaling', loss='squared_loss', max_iter=None,\n",
              "       n_iter=None, n_iter_no_change=5, penalty='l2', power_t=0.25,\n",
              "       random_state=None, shuffle=True, tol=None, validation_fraction=0.1,\n",
              "       verbose=0, warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "metadata": {
        "id": "u2UarZ2X3A9r",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "boston = load_boston()\n",
        "bos = pd.DataFrame(boston.data)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "J_vBsf983N4O",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "bos['PRICE'] = boston.target\n",
        "X = bos.drop('PRICE', axis = 1)\n",
        "Y = bos['PRICE']"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "L3s-9H1E3i6t",
        "colab_type": "code",
        "outputId": "34401904-0bd0-40e7-d1ab-a2f08d7ab725",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 197
        }
      },
      "cell_type": "code",
      "source": [
        "X.head(5)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "      <th>2</th>\n",
              "      <th>3</th>\n",
              "      <th>4</th>\n",
              "      <th>5</th>\n",
              "      <th>6</th>\n",
              "      <th>7</th>\n",
              "      <th>8</th>\n",
              "      <th>9</th>\n",
              "      <th>10</th>\n",
              "      <th>11</th>\n",
              "      <th>12</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": [
              "        0     1     2    3      4      5     6       7    8      9     10  \\\n",
              "0  0.00632  18.0  2.31  0.0  0.538  6.575  65.2  4.0900  1.0  296.0  15.3   \n",
              "1  0.02731   0.0  7.07  0.0  0.469  6.421  78.9  4.9671  2.0  242.0  17.8   \n",
              "2  0.02729   0.0  7.07  0.0  0.469  7.185  61.1  4.9671  2.0  242.0  17.8   \n",
              "3  0.03237   0.0  2.18  0.0  0.458  6.998  45.8  6.0622  3.0  222.0  18.7   \n",
              "4  0.06905   0.0  2.18  0.0  0.458  7.147  54.2  6.0622  3.0  222.0  18.7   \n",
              "\n",
              "       11    12  \n",
              "0  396.90  4.98  \n",
              "1  396.90  9.14  \n",
              "2  392.83  4.03  \n",
              "3  394.63  2.94  \n",
              "4  396.90  5.33  "
            ]
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          "metadata": {
            "tags": []
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          "execution_count": 7
        }
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    },
    {
      "metadata": {
        "id": "CJXeaH4Z3tNI",
        "colab_type": "code",
        "outputId": "27f8a5ce-a823-4cae-b93e-a2834937ce32",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        }
      },
      "cell_type": "code",
      "source": [
        "Y.head(5)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    24.0\n",
              "1    21.6\n",
              "2    34.7\n",
              "3    33.4\n",
              "4    36.2\n",
              "Name: PRICE, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "metadata": {
        "id": "3LyekJ-j3ylH",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## SPLITTING THE DATA INTO TRAIN AND TEST BEFORE DEPLOYING INTO THE MODELS "
      ]
    },
    {
      "metadata": {
        "id": "kfNECaKJ3Qbz",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "xtrain ,xtest ,ytrain ,ytest = train_test_split(X ,Y ,random_state = 0, test_size = 0.3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "uqrh1QzU3SMD",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "sc = StandardScaler()\n",
        "xtrain = sc.fit_transform(xtrain)\n",
        "xtest = sc.transform(xtest)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "KcodbzpP4AxO",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## WRITING THE FUNCTION TO IMPLEMENT THE SGD REGRESSOR"
      ]
    },
    {
      "metadata": {
        "id": "U0-8SDKs2fsL",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "def sgd(X, y, niter ,r):\n",
        "    b = 0\n",
        "    n = len(X)\n",
        "    w = np.random.normal(loc = 0.0 ,scale =1.0 ,size = (X.shape[1],))\n",
        "    for i in range(niter):\n",
        "        totalerror = []\n",
        "        for j in range(len(X)):\n",
        "            y_p = np.array(X[j]).dot(w) + b\n",
        "            error = y.iloc[j] - y_p\n",
        "            totalerror.append(error)\n",
        "            \n",
        "        w = w - r*((-2/n)*X.T.dot(totalerror))\n",
        "        b = b - r*((-2/n)*np.sum(totalerror))\n",
        "    return w ,b"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "plxKJgCs2nhJ",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "opt_w , opt_b = sgd(xtrain,ytrain,10000,0.001)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "0mhJspae6SOo",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "pF6sdJ2h2pzB",
        "colab_type": "code",
        "outputId": "28ade221-0cce-432f-da38-ce3976b02111",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "cell_type": "code",
      "source": [
        "print(\"The Optimal Coefficient is\",opt_w)\n",
        "print(\"The Optimal Intercept is\",opt_b)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The Optimal Coefficient is [-0.94864569  0.9247058  -0.21189765  0.66386768 -1.72170669  2.79213908\n",
            " -0.34721065 -3.0201566   1.31932692 -1.03947224 -2.22796961  0.57434953\n",
            " -3.40129503]\n",
            "The Optimal Intercept is 22.745480180036335\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "MYEJrmgY4brY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## OBTAINED THE COEFFICIENTS AND INTERCEPTS FOR THE SGD."
      ]
    },
    {
      "metadata": {
        "id": "U0vK_JnB3tSX",
        "colab_type": "code",
        "outputId": "c1c44251-3447-43a8-b626-cf09e0be0b82",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "predictedy = xtest.dot(opt_w) + opt_b\n",
        "err = ytest - predictedy\n",
        "MSEofsgd = (np.sum(err**2)/xtest.shape[0])\n",
        "RMSEofsgd = np.sqrt(MSEofsgd)\n",
        "print(\"MSE is\",MSEofsgd)\n",
        "print(\"RMSE is\",RMSEofsgd)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "MSE is 27.642520276585294\n",
            "RMSE is 5.257615455373785\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Lw_VOTn84k5Q",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "##USING THE SCIKIT LEARN MODEL FOR IMPLEMENTATION"
      ]
    },
    {
      "metadata": {
        "id": "LreK5StQ3xNZ",
        "colab_type": "code",
        "outputId": "fa00b58f-05ea-46f7-a823-14ddc5744f62",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "cell_type": "code",
      "source": [
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "from sklearn.linear_model import SGDRegressor\n",
        "sgd= SGDRegressor(n_iter=1000,alpha=0.01)\n",
        "sgd.fit(xtrain,ytrain)\n",
        "coef_ = sgd.coef_\n",
        "print(\"The Coefficient is\",coef_)\n",
        "intercept = sgd.intercept_\n",
        "print(\"The Intercept is\",intercept)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The Coefficient is [-0.97430289  0.98916735 -0.01229955  0.64232458 -1.74674731  2.73364115\n",
            " -0.29462013 -2.96792251  1.82947848 -1.63062996 -2.22788556  0.58173399\n",
            " -3.38414018]\n",
            "The Intercept is [22.74676436]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "nHGXDm8Y9hSM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "91ffd9e9-d6ba-46d6-851f-0cabf50879db"
      },
      "cell_type": "code",
      "source": [
        "sgd"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SGDRegressor(alpha=0.01, average=False, early_stopping=False, epsilon=0.1,\n",
              "       eta0=0.01, fit_intercept=True, l1_ratio=0.15,\n",
              "       learning_rate='invscaling', loss='squared_loss', max_iter=None,\n",
              "       n_iter=1000, n_iter_no_change=5, penalty='l2', power_t=0.25,\n",
              "       random_state=None, shuffle=True, tol=None, validation_fraction=0.1,\n",
              "       verbose=0, warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "metadata": {
        "id": "5ULQLog_4Dl1",
        "colab_type": "code",
        "outputId": "5436778b-780c-4e7a-e10e-a990a37aed5a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "y_pred = sgd.predict(xtest)\n",
        "error = ytest - y_pred\n",
        "MSE = (np.sum(error**2)/xtest.shape[0])\n",
        "RMSE = np.sqrt(MSE)\n",
        "print(\"MSE is\",MSE)\n",
        "print(\"RMSE is\",RMSE)"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "MSE is 27.338102408275493\n",
            "RMSE is 5.228585124895213\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "F9_wvwX45ALb",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "COMPARING THE WEIGHTS FROM THE SCIKIT LEARN MODEL AND WEIGHTS FROM SCRATCH"
      ]
    },
    {
      "metadata": {
        "id": "yBu-ueMM4GED",
        "colab_type": "code",
        "outputId": "15ec18e3-bdeb-4448-f908-0580683a36a1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "cell_type": "code",
      "source": [
        "fig,ax=plt.subplots()\n",
        "ax.plot(sgd.coef_)\n",
        "ax.plot(opt_w)\n",
        "plt.show()"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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O0Wkmxob7POelvvZ16DhBXloc3/nAZmptI7xl7eVf7qngH/dVYDYaPB+tH/8A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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "6i0L01_t7r5t",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "9042ade5-498f-4d6a-fd8b-ba259d098a60"
      },
      "cell_type": "code",
      "source": [
        "print(xtrain.shape[1])"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "13\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "yksiWSlC6sWi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        },
        "outputId": "bb527cc7-9d66-430f-cef6-7a47da69cbad"
      },
      "cell_type": "code",
      "source": [
        "\n",
        "plt.scatter(sgd.coef_,range(0,13))\n",
        "plt.scatter(opt_w,range(0,13))\n",
        "plt.show()"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3Ip6r1nBI357+QT317Z36zOg31dVySi+1X6qO9217+a5GALOW5RP6KknPR8RPI2JU0v2S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\nBIEOAIn4P5vSbMljGkBeAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "oV6m8bSN4H7j",
        "colab_type": "code",
        "outputId": "7acd37fe-63a2-4cdd-c70e-77fdf076b243",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        }
      },
      "cell_type": "code",
      "source": [
        "data = [[27.41,5.23], [27.3,5.22]]\n",
        "pd.DataFrame(data, columns=[\"MSE\", \"RMSE\"],index=['sgd from scratch','sgd sklearn'])"
      ],
      "execution_count": 48,
      "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>MSE</th>\n",
              "      <th>RMSE</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sgd from scratch</th>\n",
              "      <td>27.41</td>\n",
              "      <td>5.23</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sgd sklearn</th>\n",
              "      <td>27.30</td>\n",
              "      <td>5.22</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    MSE  RMSE\n",
              "sgd from scratch  27.41  5.23\n",
              "sgd sklearn       27.30  5.22"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "metadata": {
        "id": "a9T70Eap8jJo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 436
        },
        "outputId": "83d5af07-b901-4123-9df0-4fc82c64691d"
      },
      "cell_type": "code",
      "source": [
        "#comparing the weights\n",
        "ss=pd.DataFrame()\n",
        "ss['weights_of_sgdfromscratch']=sgd.coef_\n",
        "ss['sgd regressor weights']=opt_w\n",
        "ss"
      ],
      "execution_count": 47,
      "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>weights_of_sgdfromscratch</th>\n",
              "      <th>sgd regressor weights</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-0.974303</td>\n",
              "      <td>-0.948646</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.989167</td>\n",
              "      <td>0.924706</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-0.012300</td>\n",
              "      <td>-0.211898</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.642325</td>\n",
              "      <td>0.663868</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.746747</td>\n",
              "      <td>-1.721707</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>2.733641</td>\n",
              "      <td>2.792139</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>-0.294620</td>\n",
              "      <td>-0.347211</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>-2.967923</td>\n",
              "      <td>-3.020157</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1.829478</td>\n",
              "      <td>1.319327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>-1.630630</td>\n",
              "      <td>-1.039472</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>-2.227886</td>\n",
              "      <td>-2.227970</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>0.581734</td>\n",
              "      <td>0.574350</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>-3.384140</td>\n",
              "      <td>-3.401295</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    weights_of_sgdfromscratch  sgd regressor weights\n",
              "0                   -0.974303              -0.948646\n",
              "1                    0.989167               0.924706\n",
              "2                   -0.012300              -0.211898\n",
              "3                    0.642325               0.663868\n",
              "4                   -1.746747              -1.721707\n",
              "5                    2.733641               2.792139\n",
              "6                   -0.294620              -0.347211\n",
              "7                   -2.967923              -3.020157\n",
              "8                    1.829478               1.319327\n",
              "9                   -1.630630              -1.039472\n",
              "10                  -2.227886              -2.227970\n",
              "11                   0.581734               0.574350\n",
              "12                  -3.384140              -3.401295"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "metadata": {
        "id": "DjXyq8MB5Qnf",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "## DOCUMENTATION AND CONCLUSION\n",
        "###WE HAVE ONTAINED THE BOSTON DATA A TO PREDICT THE HOUSE PRICE. THE TWO MODELS WE USED ARE SGD FUNCTION WRITTEN FROM SCRATCH AND OTHER SGD REGRESSOR MODEL OF SCIKIT LEARN,.\n",
        "## WE OBTAINED THE WEGHTS AND COMAPARED THE WEIGHTS USING GRAPH AND VISUALISED IT. COMAPARED THE PERFORMANCE USING THE PANDAS DATAFRAME.\n",
        "## we plotted the weghts on the scattere plot and visualised the difference between them.\n",
        "## for comparsion of weights we also compared using the dataframe.\n",
        "##in boston data we are provided with features ['CRIM' 'ZN' 'INDUS' 'CHAS' 'NOX' 'RM' 'AGE' 'DIS' 'RAD' 'TAX' 'PTRATIO' 'B' 'LSTAT'] \n",
        " ## with these features we have the values to predict the house price , since the problem is regression we dont have the exact classs labels . we train a regression model on top of this using sgd regressor whisch is the stochastic gradient regressor with square loss and we measure the performance using the rmse metric. lower the rmse value higher the performance of the model. we predict the house price"
      ]
    },
    {
      "metadata": {
        "id": "QGU-8RrJuC1v",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}