logistic-regression-gradient-descent.ipynb

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        "<a href=\"https://colab.research.google.com/github/tozanni/Deep_Learning_Notebooks/blob/main/logistic-regression-gradient-descent.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Original notebook from: https://github.com/zillur-av/logistic-regression-gradient-descent/"
      ],
      "metadata": {
        "id": "dDJVbmwz2IXL"
      },
      "id": "dDJVbmwz2IXL"
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      "execution_count": 1,
      "metadata": {
        "id": "z8B_brdPlVT5"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import math"
      ],
      "id": "z8B_brdPlVT5"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J0FvKFbjlVT6"
      },
      "source": [
        "# Read the dataset"
      ],
      "id": "J0FvKFbjlVT6"
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          "data": {
            "text/plain": [
              "    Area  MajorAxisLength  MinorAxisLength  Eccentricity  ConvexArea  \\\n",
              "0  87524       442.246011       253.291155      0.819738       90546   \n",
              "1  75166       406.690687       243.032436      0.801805       78789   \n",
              "2  90856       442.267048       266.328318      0.798354       93717   \n",
              "3  45928       286.540559       208.760042      0.684989       47336   \n",
              "4  79408       352.190770       290.827533      0.564011       81463   \n",
              "\n",
              "     Extent  Perimeter    Class  \n",
              "0  0.758651   1184.040  Kecimen  \n",
              "1  0.684130   1121.786  Kecimen  \n",
              "2  0.637613   1208.575  Kecimen  \n",
              "3  0.699599    844.162  Kecimen  \n",
              "4  0.792772   1073.251  Kecimen  "
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              "      <td>844.162</td>\n",
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              "    <tr>\n",
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          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "df = pd.read_excel(\"https://github.com/tozanni/Deep_Learning_Notebooks/raw/main/Raisin_Dataset.xlsx\")\n",
        "df.head()"
      ],
      "id": "VgJ_FXA_lVT7"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y-HzFU3ClVT7"
      },
      "source": [
        "### Check the classes\n",
        "\n",
        "We have 2 classes."
      ],
      "id": "Y-HzFU3ClVT7"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "RuTFwCwXlVT7",
        "outputId": "55de00c3-9602-4823-9bc9-720109a3dab4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array(['Kecimen', 'Besni'], dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "df[\"Class\"].unique()"
      ],
      "id": "RuTFwCwXlVT7"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1glqtUYwlVT8"
      },
      "source": [
        "## Separate two classes"
      ],
      "id": "1glqtUYwlVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "pOrqDn7rlVT8"
      },
      "outputs": [],
      "source": [
        "dfs = [x for _, x in df.groupby('Class')]\n",
        "df0 = dfs[1].reset_index(drop=True)\n",
        "df1 = dfs[0].drop(columns=[\"Class\"]).reset_index(drop=True)"
      ],
      "id": "pOrqDn7rlVT8"
    },
    {
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        "colab": {
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          "data": {
            "text/plain": [
              "    Area  MajorAxisLength  MinorAxisLength  Eccentricity  ConvexArea  \\\n",
              "0  87524       442.246011       253.291155      0.819738       90546   \n",
              "1  75166       406.690687       243.032436      0.801805       78789   \n",
              "2  90856       442.267048       266.328318      0.798354       93717   \n",
              "3  45928       286.540559       208.760042      0.684989       47336   \n",
              "4  79408       352.190770       290.827533      0.564011       81463   \n",
              "\n",
              "     Extent  Perimeter    Class  \n",
              "0  0.758651   1184.040  Kecimen  \n",
              "1  0.684130   1121.786  Kecimen  \n",
              "2  0.637613   1208.575  Kecimen  \n",
              "3  0.699599    844.162  Kecimen  \n",
              "4  0.792772   1073.251  Kecimen  "
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              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Area</th>\n",
              "      <th>MajorAxisLength</th>\n",
              "      <th>MinorAxisLength</th>\n",
              "      <th>Eccentricity</th>\n",
              "      <th>ConvexArea</th>\n",
              "      <th>Extent</th>\n",
              "      <th>Perimeter</th>\n",
              "      <th>Class</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>87524</td>\n",
              "      <td>442.246011</td>\n",
              "      <td>253.291155</td>\n",
              "      <td>0.819738</td>\n",
              "      <td>90546</td>\n",
              "      <td>0.758651</td>\n",
              "      <td>1184.040</td>\n",
              "      <td>Kecimen</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>75166</td>\n",
              "      <td>406.690687</td>\n",
              "      <td>243.032436</td>\n",
              "      <td>0.801805</td>\n",
              "      <td>78789</td>\n",
              "      <td>0.684130</td>\n",
              "      <td>1121.786</td>\n",
              "      <td>Kecimen</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>90856</td>\n",
              "      <td>442.267048</td>\n",
              "      <td>266.328318</td>\n",
              "      <td>0.798354</td>\n",
              "      <td>93717</td>\n",
              "      <td>0.637613</td>\n",
              "      <td>1208.575</td>\n",
              "      <td>Kecimen</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>45928</td>\n",
              "      <td>286.540559</td>\n",
              "      <td>208.760042</td>\n",
              "      <td>0.684989</td>\n",
              "      <td>47336</td>\n",
              "      <td>0.699599</td>\n",
              "      <td>844.162</td>\n",
              "      <td>Kecimen</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>79408</td>\n",
              "      <td>352.190770</td>\n",
              "      <td>290.827533</td>\n",
              "      <td>0.564011</td>\n",
              "      <td>81463</td>\n",
              "      <td>0.792772</td>\n",
              "      <td>1073.251</td>\n",
              "      <td>Kecimen</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "  @keyframes spin {\n",
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              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
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              "\n",
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              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "df0",
              "summary": "{\n  \"name\": \"df0\",\n  \"rows\": 450,\n  \"fields\": [\n    {\n      \"column\": \"Area\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 17727,\n        \"min\": 25387,\n        \"max\": 180898,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          73311,\n          67874,\n          90176\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MajorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 59.61149355578842,\n        \"min\": 225.629541,\n        \"max\": 843.9566534,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          391.8675067,\n          360.0234655,\n          390.207341\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MinorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 34.058657169114454,\n        \"min\": 143.7108718,\n        \"max\": 326.8987235,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          239.6017637,\n          243.2719738,\n          294.7622385\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Eccentricity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.09236172917880658,\n        \"min\": 0.348729642,\n        \"max\": 0.923770364,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          0.791294159,\n          0.737166231,\n          0.65526509\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"ConvexArea\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 19005,\n        \"min\": 26139,\n        \"max\": 221396,\n        \"num_unique_values\": 447,\n        \"samples\": [\n          96072,\n          84531,\n          91793\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Extent\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.04344223016498103,\n        \"min\": 0.454188929,\n        \"max\": 0.835454545,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          0.689966401,\n          0.678319442,\n          0.762549046\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Perimeter\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 150.305531290128,\n        \"min\": 619.074,\n        \"max\": 2253.557,\n        \"num_unique_values\": 450,\n        \"samples\": [\n          1046.52,\n          1035.277,\n          1136.669\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Class\",\n      \"properties\": {\n        \"dtype\": \"category\",\n        \"num_unique_values\": 1,\n        \"samples\": [\n          \"Kecimen\"\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "df0.head()"
      ],
      "id": "Q6JyM3yplVT8"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SYxxaJWqlVT8"
      },
      "source": [
        "### Assign class  number to each class"
      ],
      "id": "SYxxaJWqlVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "2Pb7Oc0slVT8"
      },
      "outputs": [],
      "source": [
        "df0[\"Class\"] = 0\n",
        "df1[\"Class\"] = 1"
      ],
      "id": "2Pb7Oc0slVT8"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KEH1OCnBlVT8"
      },
      "source": [
        "# Prepare train and test sets\n",
        "\n",
        "80\\% in train and 20\\% in test"
      ],
      "id": "KEH1OCnBlVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "AhkHhQhklVT8"
      },
      "outputs": [],
      "source": [
        "train_df0 = df0.iloc[0: int(len(df0)*0.8)]\n",
        "train_df1 = df1.iloc[0: int(len(df1)*0.8)]"
      ],
      "id": "AhkHhQhklVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "_mxneWKolVT8",
        "outputId": "182ee168-26d4-4536-9394-5a323cb043f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Area  MajorAxisLength  MinorAxisLength  Eccentricity  ConvexArea  \\\n",
              "0     87524       442.246011       253.291155      0.819738       90546   \n",
              "1     75166       406.690687       243.032436      0.801805       78789   \n",
              "2     90856       442.267048       266.328318      0.798354       93717   \n",
              "3     45928       286.540559       208.760042      0.684989       47336   \n",
              "4     79408       352.190770       290.827533      0.564011       81463   \n",
              "..      ...              ...              ...           ...         ...   \n",
              "715   56244       398.802452       182.844046      0.888703       58530   \n",
              "716  142239       614.834478       297.735347      0.874928      148078   \n",
              "717   78632       407.940329       245.821198      0.798050       79715   \n",
              "718   93430       467.637119       258.947168      0.832693       98337   \n",
              "719   97583       522.786556       241.940773      0.886468      101231   \n",
              "\n",
              "       Extent  Perimeter  \n",
              "0    0.758651   1184.040  \n",
              "1    0.684130   1121.786  \n",
              "2    0.637613   1208.575  \n",
              "3    0.699599    844.162  \n",
              "4    0.792772   1073.251  \n",
              "..        ...        ...  \n",
              "715  0.656366   1008.134  \n",
              "716  0.643516   1553.114  \n",
              "717  0.689011   1068.727  \n",
              "718  0.712988   1258.966  \n",
              "719  0.725983   1298.731  \n",
              "\n",
              "[720 rows x 7 columns]"
            ],
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Area</th>\n",
              "      <th>MajorAxisLength</th>\n",
              "      <th>MinorAxisLength</th>\n",
              "      <th>Eccentricity</th>\n",
              "      <th>ConvexArea</th>\n",
              "      <th>Extent</th>\n",
              "      <th>Perimeter</th>\n",
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              "      <th>0</th>\n",
              "      <td>87524</td>\n",
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              "      <td>253.291155</td>\n",
              "      <td>0.819738</td>\n",
              "      <td>90546</td>\n",
              "      <td>0.758651</td>\n",
              "      <td>1184.040</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>75166</td>\n",
              "      <td>406.690687</td>\n",
              "      <td>243.032436</td>\n",
              "      <td>0.801805</td>\n",
              "      <td>78789</td>\n",
              "      <td>0.684130</td>\n",
              "      <td>1121.786</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>90856</td>\n",
              "      <td>442.267048</td>\n",
              "      <td>266.328318</td>\n",
              "      <td>0.798354</td>\n",
              "      <td>93717</td>\n",
              "      <td>0.637613</td>\n",
              "      <td>1208.575</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>45928</td>\n",
              "      <td>286.540559</td>\n",
              "      <td>208.760042</td>\n",
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              "      <td>0.699599</td>\n",
              "      <td>844.162</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>79408</td>\n",
              "      <td>352.190770</td>\n",
              "      <td>290.827533</td>\n",
              "      <td>0.564011</td>\n",
              "      <td>81463</td>\n",
              "      <td>0.792772</td>\n",
              "      <td>1073.251</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>715</th>\n",
              "      <td>56244</td>\n",
              "      <td>398.802452</td>\n",
              "      <td>182.844046</td>\n",
              "      <td>0.888703</td>\n",
              "      <td>58530</td>\n",
              "      <td>0.656366</td>\n",
              "      <td>1008.134</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>716</th>\n",
              "      <td>142239</td>\n",
              "      <td>614.834478</td>\n",
              "      <td>297.735347</td>\n",
              "      <td>0.874928</td>\n",
              "      <td>148078</td>\n",
              "      <td>0.643516</td>\n",
              "      <td>1553.114</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>717</th>\n",
              "      <td>78632</td>\n",
              "      <td>407.940329</td>\n",
              "      <td>245.821198</td>\n",
              "      <td>0.798050</td>\n",
              "      <td>79715</td>\n",
              "      <td>0.689011</td>\n",
              "      <td>1068.727</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>718</th>\n",
              "      <td>93430</td>\n",
              "      <td>467.637119</td>\n",
              "      <td>258.947168</td>\n",
              "      <td>0.832693</td>\n",
              "      <td>98337</td>\n",
              "      <td>0.712988</td>\n",
              "      <td>1258.966</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>719</th>\n",
              "      <td>97583</td>\n",
              "      <td>522.786556</td>\n",
              "      <td>241.940773</td>\n",
              "      <td>0.886468</td>\n",
              "      <td>101231</td>\n",
              "      <td>0.725983</td>\n",
              "      <td>1298.731</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>720 rows × 7 columns</p>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3bbe3317-3f29-478c-b81d-b43f03ea10d7')\"\n",
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              "            style=\"display:none;\">\n",
              "\n",
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              "    </button>\n",
              "\n",
              "  <style>\n",
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              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "        document.querySelector('#df-3bbe3317-3f29-478c-b81d-b43f03ea10d7 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-3bbe3317-3f29-478c-b81d-b43f03ea10d7');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
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              "  </div>\n",
              "\n",
              "\n",
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              "  [theme=dark] .colab-df-quickchart {\n",
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              "  .colab-df-quickchart {\n",
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              "  .colab-df-quickchart:hover {\n",
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              "  .colab-df-quickchart-complete:disabled,\n",
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              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
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              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
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              "  @keyframes spin {\n",
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              "    60% {\n",
              "      border-color: transparent;\n",
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              "    80% {\n",
              "      border-color: transparent;\n",
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              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
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              "    (() => {\n",
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              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "\n",
              "  <div id=\"id_0c99c469-f0ca-4208-9ce9-ea49ce76a820\">\n",
              "    <style>\n",
              "      .colab-df-generate {\n",
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              "        border: none;\n",
              "        border-radius: 50%;\n",
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              "        fill: #1967D2;\n",
              "        height: 32px;\n",
              "        padding: 0 0 0 0;\n",
              "        width: 32px;\n",
              "      }\n",
              "\n",
              "      .colab-df-generate:hover {\n",
              "        background-color: #E2EBFA;\n",
              "        box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "        fill: #174EA6;\n",
              "      }\n",
              "\n",
              "      [theme=dark] .colab-df-generate {\n",
              "        background-color: #3B4455;\n",
              "        fill: #D2E3FC;\n",
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              "      [theme=dark] .colab-df-generate:hover {\n",
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              "    </style>\n",
              "    <button class=\"colab-df-generate\" onclick=\"generateWithVariable('X_train_data')\"\n",
              "            title=\"Generate code using this dataframe.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    </button>\n",
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              "\n",
              "      buttonEl.onclick = () => {\n",
              "        google.colab.notebook.generateWithVariable('X_train_data');\n",
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              "\n",
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "X_train_data",
              "summary": "{\n  \"name\": \"X_train_data\",\n  \"rows\": 720,\n  \"fields\": [\n    {\n      \"column\": \"Area\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 38921,\n        \"min\": 25387,\n        \"max\": 223075,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          39724,\n          136340,\n          111450\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MajorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 117.01963217861893,\n        \"min\": 225.629541,\n        \"max\": 997.2919406,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          271.6656922,\n          722.8539172,\n          478.3109708\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MinorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 49.30838486164842,\n        \"min\": 144.618672,\n        \"max\": 440.4971275,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          189.484632,\n          311.3413551,\n          298.630592\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Eccentricity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.09335524261850119,\n        \"min\": 0.348729642,\n        \"max\": 0.96212444,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          0.716592623,\n          0.902489762,\n          0.781149506\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"ConvexArea\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 40763,\n        \"min\": 26139,\n        \"max\": 278217,\n        \"num_unique_values\": 716,\n        \"samples\": [\n          71843,\n          62130,\n          50880\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Extent\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.054117242772257504,\n        \"min\": 0.379856115,\n        \"max\": 0.835454545,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          0.724282537,\n          0.529774048,\n          0.690092879\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Perimeter\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 274.7487461054546,\n        \"min\": 619.074,\n        \"max\": 2697.753,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          781.97,\n          2098.263,\n          1298.188\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "X_train_data = pd.concat([train_df0.drop(columns=[\"Class\"]), train_df1.drop(columns=[\"Class\"])]).reset_index(drop=True)\n",
        "X_train_data"
      ],
      "id": "_mxneWKolVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "hO-Xlm9AlVT8",
        "outputId": "9f039abb-e443-4466-96b4-e5e68456d81b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
              "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "y_train = pd.concat([train_df0[\"Class\"], train_df1[\"Class\"]]).to_numpy()\n",
        "y_train"
      ],
      "id": "hO-Xlm9AlVT8"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "YFdmPvIalVT9"
      },
      "outputs": [],
      "source": [
        "test_df0 = df0.iloc[int(len(df0)*0.8):]\n",
        "test_df1 = df1.iloc[int(len(df1)*0.8):]"
      ],
      "id": "YFdmPvIalVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "5lV1wRtflVT9"
      },
      "outputs": [],
      "source": [
        "X_test_data = pd.concat([test_df0.drop(columns=[\"Class\"]), test_df1.drop(columns=[\"Class\"])]).reset_index(drop=True)\n",
        "y_test = pd.concat([test_df0[\"Class\"], test_df1[\"Class\"]]).to_numpy()"
      ],
      "id": "5lV1wRtflVT9"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oAuUK-NClVT9"
      },
      "source": [
        "# Standardize the dataset\n",
        "\n",
        "Before preparing the model, the entire dataset need to be standardized. Only train set mean and standard deviation are used to standardize the dataset to avoid potential bias. Each feature/attribute $(X_i)$ is subtracted by its mean $\\mu$ and divided by its standard deviation $\\sigma$.\n",
        "\n",
        "$\\mu = \\frac{1}{N} * X_i$\\\n",
        "$X_i = (X_i - \\mu) / \\sigma$"
      ],
      "id": "oAuUK-NClVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "vp7USqcTlVT9"
      },
      "outputs": [],
      "source": [
        "mean_train = X_train_data.mean()\n",
        "std_train = X_train_data.std()"
      ],
      "id": "vp7USqcTlVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "V2PPkqsylVT9",
        "outputId": "4d724b7c-0aaa-4e01-8ced-65ce005dacf3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Area               88043.401389\n",
              "MajorAxisLength      432.215772\n",
              "MinorAxisLength      254.705362\n",
              "Eccentricity           0.780984\n",
              "ConvexArea         91495.638889\n",
              "Extent                 0.698941\n",
              "Perimeter           1169.716692\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "mean_train"
      ],
      "id": "V2PPkqsylVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "CWnUI6lSlVT9",
        "outputId": "55a5d6b1-412b-4a36-eb91-522ec8866db6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Area               38921.340363\n",
              "MajorAxisLength      117.019632\n",
              "MinorAxisLength       49.308385\n",
              "Eccentricity           0.093355\n",
              "ConvexArea         40763.058741\n",
              "Extent                 0.054117\n",
              "Perimeter            274.748746\n",
              "dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "std_train"
      ],
      "id": "CWnUI6lSlVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "FsRYp3BglVT9",
        "outputId": "af33f46c-0f5e-4af2-e312-0364c2077115",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Area  MajorAxisLength  MinorAxisLength  Eccentricity  ConvexArea  \\\n",
              "0 -0.013345         0.085714        -0.028681      0.415126   -0.023297   \n",
              "1 -0.330857        -0.218127        -0.236733      0.223030   -0.311719   \n",
              "2  0.072264         0.085894         0.235720      0.186058    0.054494   \n",
              "3 -1.082065        -1.244878        -0.931795     -1.028276   -1.083325   \n",
              "4 -0.221868        -0.683860         0.732577     -2.324163   -0.246121   \n",
              "\n",
              "     Extent  Perimeter  \n",
              "0  1.103335   0.052132  \n",
              "1 -0.273694  -0.174453  \n",
              "2 -1.133249   0.141432  \n",
              "3  0.012163  -1.184918  \n",
              "4  1.733843  -0.351105  "
            ],
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            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "X_train_standard",
              "summary": "{\n  \"name\": \"X_train_standard\",\n  \"rows\": 720,\n  \"fields\": [\n    {\n      \"column\": \"Area\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -1.609821265250347,\n        \"max\": 3.4693460541362047,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          -1.2414629336467848,\n          1.2408770653913515,\n          0.6013821310527407\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MajorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -1.7653980521780206,\n        \"max\": 4.828900573048671,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          -1.3719926864037513,\n          2.4836699626747007,\n          0.3939099638846749\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MinorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -2.2326160248938587,\n        \"max\": 3.7679547974964596,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          -1.322710739496926,\n          1.1486077480566779,\n          0.890826781682208\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Eccentricity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -4.6302116442759305,\n        \"max\": 1.9403330920990258,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          -0.6897475558981369,\n          1.3015400652981766,\n          0.0017710047017585589\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"ConvexArea\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -1.6033300961206742,\n        \"max\": 4.580651376014335,\n        \"num_unique_values\": 716,\n        \"samples\": [\n          -0.4821188472117712,\n          -0.7203983164191091,\n          -0.996383493870211\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Extent\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -5.896180215734562,\n        \"max\": 2.522549317795122,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          0.4682686060477207,\n          -3.1259368455964673,\n          -0.16350153316430208\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Perimeter\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0,\n        \"min\": -2.0041681699079277,\n        \"max\": 5.5615770044200294,\n        \"num_unique_values\": 720,\n        \"samples\": [\n          -1.4112773840206756,\n          3.3796198217295474,\n          0.46759561291691304\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "X_train_standard = (X_train_data - mean_train)/ std_train\n",
        "X_train_standard.head()"
      ],
      "id": "FsRYp3BglVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "id": "ro5ffG6alVT9",
        "outputId": "d03e15d7-2fed-4eba-9dde-90b6be72d21e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(720, 7)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "X_train_standard = X_train_standard.to_numpy()\n",
        "X_train_standard.shape"
      ],
      "id": "ro5ffG6alVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "zd_S9kgglVT9",
        "outputId": "13da70ad-7a55-4238-8185-7d97657cb169",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(720, 8)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "X_train = np.hstack([np.ones((X_train_standard.shape[0],1)), X_train_standard]) # add bias term\n",
        "X_train.shape"
      ],
      "id": "zd_S9kgglVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "24eeiRVQlVT9",
        "outputId": "a01902cc-33fb-4039-a741-5fae76d43fea",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       Area  MajorAxisLength  MinorAxisLength  Eccentricity  ConvexArea  \\\n",
              "0 -1.008043        -0.854138        -1.305133      0.413987   -0.972661   \n",
              "1 -1.002134        -1.254607        -0.687215     -1.579456   -0.996408   \n",
              "2 -0.600555        -0.577963        -0.525359     -0.025955   -0.588073   \n",
              "3  0.393964         0.243161         0.675094     -0.005231    0.345248   \n",
              "4 -0.361534        -0.623341         0.174981     -1.078837   -0.396011   \n",
              "\n",
              "     Extent  Perimeter  \n",
              "0 -0.694778  -0.879715  \n",
              "1  0.292508  -1.194003  \n",
              "2 -0.796336  -0.633396  \n",
              "3  0.517888   0.220261  \n",
              "4  1.031061  -0.553115  "
            ],
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              "      <td>-0.025955</td>\n",
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              "      <td>-0.796336</td>\n",
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              "      <td>0.243161</td>\n",
              "      <td>0.675094</td>\n",
              "      <td>-0.005231</td>\n",
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              "      <td>0.517888</td>\n",
              "      <td>0.220261</td>\n",
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              "      <td>-0.623341</td>\n",
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              "      <td>-1.078837</td>\n",
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              "      const quickchartButtonEl =\n",
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            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "X_test_standard",
              "summary": "{\n  \"name\": \"X_test_standard\",\n  \"rows\": 180,\n  \"fields\": [\n    {\n      \"column\": \"Area\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0127651542229141,\n        \"min\": -1.5707424466433149,\n        \"max\": 3.7769408051969457,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.22978143366618478,\n          -0.9439397781770736,\n          0.24281277373535823\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MajorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.9586478273564378,\n        \"min\": -1.59643705450696,\n        \"max\": 4.421881101928658,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.15996808369854512,\n          -0.7022171278857976,\n          0.16721121337495443\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"MinorAxisLength\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0699449011361306,\n        \"min\": -2.251026690798798,\n        \"max\": 4.818042954820642,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.168341662924883,\n          -1.317015846005933,\n          0.4781062239697513\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Eccentricity\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.8266984436665562,\n        \"min\": -2.930230030511174,\n        \"max\": 1.8220516149127444,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          0.23641398120299267,\n          0.6353821586218649,\n          0.07276974900459254\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"ConvexArea\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 1.0029767946948605,\n        \"min\": -1.5427850811918458,\n        \"max\": 3.6208607908946098,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.2368968175405521,\n          -0.9456267532349817,\n          0.2547002465432372\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Extent\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.9400181914273081,\n        \"min\": -5.262414871399942,\n        \"max\": 1.7092318288530663,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.8092191309188183,\n          -0.7011332658533017,\n          -0.1708413934316047\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Perimeter\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.9827477424258186,\n        \"min\": -1.7867295069592342,\n        \"max\": 4.3032491506968915,\n        \"num_unique_values\": 180,\n        \"samples\": [\n          -0.20422182980638845,\n          -0.9921999482466599,\n          0.3095129988352842\n        ],\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "X_test_standard = (X_test_data - mean_train)/ std_train\n",
        "X_test_standard.head()"
      ],
      "id": "24eeiRVQlVT9"
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "myzW2XHKlVT-",
        "outputId": "48611a5e-dcea-412f-f34d-c0bf42cb031e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(180, 7)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "X_test_standard = X_test_standard.to_numpy()\n",
        "X_test_standard.shape"
      ],
      "id": "myzW2XHKlVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "BDoQukCTlVT-",
        "outputId": "a6bbeaf7-3f02-4997-859f-aa3a39599c59",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(180, 8)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ],
      "source": [
        "X_test = np.hstack([np.ones((X_test_standard.shape[0],1)), X_test_standard]) # add bias term\n",
        "X_test.shape"
      ],
      "id": "BDoQukCTlVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D_DS4i42lVT-"
      },
      "source": [
        "# Prepare the Logistic Regression algorithm\n",
        "\n",
        "Steps to follow:\n",
        "\n",
        "* Initialize the weights\n",
        "* Make prediction using current weights\n",
        "* Calculate gradient of the weights and update the weights\n",
        "* Calculate cost function\n",
        "* Repeat steps 2-4 until convergence\n",
        "\n",
        "All of the above steps must be done only for train set. Read bellow cells to understand each step."
      ],
      "id": "D_DS4i42lVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M4MiAOzLlVT-"
      },
      "source": [
        "## Sigmoid function\n",
        "$$sigmoid(x) = \\frac {1} {1+exp(-x)} $$"
      ],
      "id": "M4MiAOzLlVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "CjQ0QZaSlVT-"
      },
      "outputs": [],
      "source": [
        "def sigmoid(x):\n",
        "    return 1/(1 + np.exp(-x))"
      ],
      "id": "CjQ0QZaSlVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gzv5So17lVT-"
      },
      "source": [
        "## Cost Function\n",
        "\n",
        " $$ cost = - y*log(\\hat{y}) - (1 - y) * log(1-\\hat{y}) $$"
      ],
      "id": "Gzv5So17lVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "uWA7Qu-xlVT-"
      },
      "outputs": [],
      "source": [
        "def cost(y_truth, y_proba):\n",
        "    loss = - y_truth*np.log(y_proba) - (1- y_truth)*np.log(1 - y_proba)\n",
        "    return loss"
      ],
      "id": "uWA7Qu-xlVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5YVgG2G4lVT-"
      },
      "source": [
        "## Compute Gradient\n",
        "For Logistic Regression, the gradient of the weight is :\n",
        "$$ gradient(w) = (\\hat{y} - y)*X $$"
      ],
      "id": "5YVgG2G4lVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "XrAoXNGQlVT-"
      },
      "outputs": [],
      "source": [
        "def gradient_compute(X, y, y_proba):\n",
        "    '''\n",
        "    X: Input Feature Array of NxD shape\n",
        "    y: ground truth output of N shape\n",
        "    y_proba: probability of N shape\n",
        "    '''\n",
        "    assert y.ndim == 1, \"y should be one dimensional\"\n",
        "    return np.dot((y_proba - y), X)"
      ],
      "id": "XrAoXNGQlVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T0nBJTMIlVT-"
      },
      "source": [
        "## Probability prediction\n",
        "$$\\hat{y} = sigmoid(w^T . x)$$"
      ],
      "id": "T0nBJTMIlVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "wpJq7v_LlVT-"
      },
      "outputs": [],
      "source": [
        "def probability(w, X):\n",
        "    y_proba = np.array([])\n",
        "    for i in range(len(X)):\n",
        "        proba = sigmoid(np.dot(w, X[i]))\n",
        "        y_proba = np.append(y_proba, proba)\n",
        "    return y_proba"
      ],
      "id": "wpJq7v_LlVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7om-jBYIlVT-"
      },
      "source": [
        "## Label Prediction\n",
        "\n",
        "After computing necessary parameters, each instance x is tested.\n",
        "\n",
        "$$ probability = sigmoid(w^T.x) $$\n",
        "\n",
        "This equation gives the probability between 0 and 1. Then, if it is greater than 0.5, it will be defined as class 1, and if it is less than 0.5, it will be defined as class 0."
      ],
      "id": "7om-jBYIlVT-"
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "67nm5rMclVT-"
      },
      "outputs": [],
      "source": [
        "def prediction(y_proba):\n",
        "    y_pred = np.array([], dtype=np.int16)\n",
        "\n",
        "    for i in range(len(y_proba)):\n",
        "        if y_proba[i] > 0.5:\n",
        "            pred = 1\n",
        "        else:\n",
        "            pred = 0\n",
        "        y_pred =np.append(y_pred, pred)\n",
        "    return y_pred"
      ],
      "id": "67nm5rMclVT-"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NN1I_nKNlVT_"
      },
      "source": [
        "# Offline Training Gradient Descent\n",
        "\n",
        "In offline training, we use the entire dataset at every iteration. After one forward pass using the entire training data, the weights get updated.\n",
        "$$ w = w - learning\\_rate*gradient(w) $$"
      ],
      "id": "NN1I_nKNlVT_"
    },
    {
      "cell_type": "code",
      "execution_count": 26,
      "metadata": {
        "scrolled": false,
        "id": "w9Fo0JR_lVT_"
      },
      "outputs": [],
      "source": [
        "def fit(X, y, epochs=10, learning_rate=0.01):\n",
        "    N = X.shape[0]                     # number of training samples\n",
        "    w = np.ones((1, X_train.shape[1])) # initialize the weights\n",
        "    cost_list = []\n",
        "    old_cost = 100\n",
        "    for k in range(epochs):\n",
        "        y_proba = probability(w, X)\n",
        "        w = w - learning_rate* gradient_compute(X, y, y_proba) # update the weights after one epoch\n",
        "\n",
        "        loss = 0\n",
        "        total_cost = 0\n",
        "        for i in range(N):\n",
        "            loss += cost(y[i], y_proba[i])\n",
        "        total_cost = loss / N\n",
        "        cost_list.append(total_cost)\n",
        "    return w, cost_list"
      ],
      "id": "w9Fo0JR_lVT_"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HYvGEiX1lVUC"
      },
      "source": [
        "## Training"
      ],
      "id": "HYvGEiX1lVUC"
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {
        "id": "zFjUcbNGlVUC",
        "outputId": "d6066385-ad42-467f-c1f5-0daf054c5bf2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 503
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Weights: [[ 0.54462583  0.64393505  0.74900803  0.40164323  1.09063782  0.65710503\n",
            "  -0.01551585  0.77141872]]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Loss')"
            ]
          },
          "metadata": {},
          "execution_count": 50
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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3+MBCKsHRrDKcy68QOw4REZEoWIDMjJuDFcYEuwPgUSAiIjJfLEBm6Jlrt8RvScnD1eoGccMQERGJgAXIDEX49EB/TwfUN+mwLpGPxyAiIvPDAmSGJBIJ/jiiFwDg34cyUV3fJHIiIiKi7sUCZKbGh3jAz9kW5TWN+OoIjwIREZF5YQEyUzKpBH8a2XwUaM3+TNQ1akVORERE1H1YgMzYIwO94KWyRkllPb45niN2HCIiom7DAmTGLGVS/HGEPwDgH/su8fEYRERkNliAzNwTEWq42CuQV16LzSfyxI5DRETULViAzJyVpQzPDfMDAKzamwGtThA5ERERUddjASJMifKBysYSmaXV+Ol0gdhxiIiIuhwLEMFWYYGZQ5uPAn22Jx06HgUiIiITxwJEAIDp0b6wU1jgfGElEs4Xix2HiIioS7EAEQBAaWOJqdE+AIAVe9IhCDwKREREposFiPSevdcPVpZSnMwpx4H0UrHjEBERdRkWINJztlPgqUhvAMCKX9NFTkNERNR1WICohVnD/WEpk+BIZhmOZZWJHYeIiKhLsABRCx5KazwW3hMAjwIREZHpYgGim/xpRABkUgn2XSjB6VyN2HGIiIg6HQsQ3cTbyQYTQj0BACv38CgQERGZHhYgatXzI3sBAHacLcSFokqR0xAREXUuFiBqVW83e4wLdgfQPDs0ERGRKWEBoluac18AAGDryXxcvlItchoiIqLOwwJEtxTspcTIvi7QCcDqfRlixyEiIuo0LEB0Wy/c33wU6LukXBRoakVOQ0RE1DlYgOi2wn0ccY+/Ixq1Av6x75LYcYiIiDoFCxDd0Qv39wYA/PdoNvLKeRSIiIiMHwsQ3dGQXk6I9ndCQ5MOH/+SJnYcIiKiDmMBojuSSCRY8GAgAGDziTycy68QOREREVHHsADRXRnQU4WHQz0hCMD7O86LHYeIiKhDWIDorr08ui8sZRL8dqEEBy6Wih2HiIio3ViA6K55O9lgSpQPACB+eyp0OkHkRERERO3DAkRt8sL9AbBXWOBsfgV+PJUvdhwiIqJ2YQGiNnGyU2D2tQelfrQzDfVNWpETERERtR0LELXZzKF+cHNQIPdqLdYnXhY7DhERUZuxAFGbWctliHugDwBgxZ50aGobRU5ERETUNixA1C6PDuqJ3q52KK9p5INSiYjI6LAAUbtYyKR4dWzz5IhfHMhEPh+RQURERoQFiNptVD9XRPo5or5Jh092XRA7DhER0V1jAaJ2k0gkWDCu+SjQ98m5OF/IR2QQEZFxYAGiDhno3QMPhrhDJwAfbOcjMoiIyDiwAFGHvTwmEBZSCfaklSAx44rYcYiIiO6IBYg6zM/ZFk9HeQPgIzKIiMg4sABRp3hxVG/YymU4lavBT6cLxI5DRER0WyxA1Cmc7RSYNfx/j8hoaNKJnIiIiOjWDKIArVy5Er6+vrCyskJUVBSOHj16V9tt2LABEokEkyZNarFcEAQsXLgQHh4esLa2RkxMDC5evNgFyen3/m+YH1zsFcguq8F/j/ARGUREZLhEL0AbN25EXFwcFi1ahOTkZISGhmLMmDEoLi6+7XZZWVmYP38+hg0bdtN7H374IZYtW4bVq1fjyJEjsLW1xZgxY1BXV9dVwyAAtgoLzIvpDQBY9ms6Kuv4iAwiIjJMohegJUuW4LnnnsOMGTMQFBSE1atXw8bGBl988cUtt9FqtZgyZQreeecd+Pv7t3hPEAQsXboUb775JiZOnIgBAwZg3bp1yM/Px5YtW7p4NBQboYa/iy3KqhuwLIFH3YiIyDCJWoAaGhqQlJSEmJgY/TKpVIqYmBgkJibecrvFixfD1dUVzz777E3vZWZmorCwsMVnKpVKREVF3fIz6+vrUVFR0eJF7WMhk+Kth4IAAF8czEJqAf8uiYjI8IhagEpLS6HVauHm5tZiuZubGwoLC1vd5sCBA/j888+xZs2aVt+/vl1bPjM+Ph5KpVL/UqvVbR0K/c59fV0xtr87tDoBb245w9viiYjI4Ih+CqwtKisrMXXqVKxZswbOzs6d9rkLFiyARqPRv3Jycjrts83VwoeDYCOXIenyVXyXlCt2HCIiohYsxPxyZ2dnyGQyFBUVtVheVFQEd3f3m9bPyMhAVlYWHn74Yf0yna75dmsLCwukpaXptysqKoKHh0eLzwwLC2s1h0KhgEKh6Ohw6Hc8Vdb4S0wf/PXnVMRvT8UDQW7oYSsXOxYREREAkY8AyeVyhIeHIyEhQb9Mp9MhISEB0dHRN60fGBiI06dPIyUlRf+aMGEC7rvvPqSkpECtVsPPzw/u7u4tPrOiogJHjhxp9TOp6zwz1BeB7va4WtOI9/mcMCIiMiCiHgECgLi4OEyfPh0RERGIjIzE0qVLUV1djRkzZgAApk2bBi8vL8THx8PKygrBwcEttlepVADQYvm8efPw3nvvoXfv3vDz88Nbb70FT0/Pm+YLoq5lKZPivUnBeGx1IjYez8HjET0R4esodiwiIiLxC1BsbCxKSkqwcOFCFBYWIiwsDDt27NBfxJydnQ2ptG0Hql555RVUV1dj1qxZKC8vx7333osdO3bAysqqK4ZAtxHh64jYCDU2Hs/Bm1vO4McX7oWlzKguPSMiIhMkEQSBt+jcoKKiAkqlEhqNBg4ODmLHMXpl1Q24/+O9KK9pxBsP9sNzw/3vvBEREVEbteX3N/+vOHU5R1s5FowLBAB8svsCCjS1IiciIiJzxwJE3eLxcDXCfXqgpkGLxT+eEzsOERGZORYg6hZSqQTvTQqGTCrB9jOF2JN2+2e9ERERdSUWIOo2/TwcMHOoLwBg0Q9nUdeoFTcQERGZLRYg6lbzYvrAQ2mF7LIarNyTLnYcIiIyUyxA1K1sFRZY9HDzw1JX78tARkmVyImIiMgcsQBRtxvT3x339XVBo1bAwh/OgDMxEBFRd2MBom4nkUjwzoRgKCykOJh+BVtP5osdiYiIzAwLEInC28kGL9wfAAB476dUVNQ1ipyIiIjMCQsQiea54f7wd7FFSWU9Pt6ZJnYcIiIyI+0qQDk5OcjNzdX/+ejRo5g3bx7++c9/dlowMn0KCxnem9j8ENt1hy/jyKUrIiciIiJz0a4C9PTTT2PPnj0AgMLCQjzwwAM4evQo3njjDSxevLhTA5JpGxLgjCcHqyEIwEvfnkRVfZPYkYiIyAy0qwCdOXMGkZGRAIBvvvkGwcHBOHToEL766iusXbu2M/ORGXjzoSD07GGN3Ku1eJePySAiom7QrgLU2NgIhUIBANi9ezcmTJgAAAgMDERBQUHnpSOzYKewwMePh0IiATYez8Huc0ViRyIiIhPXrgLUv39/rF69Gvv378euXbswduxYAEB+fj6cnJw6NSCZhyh/Jzw3zB8A8NqmU7hSVS9yIiIiMmXtKkAffPAB/vGPf2DkyJF46qmnEBoaCgDYunWr/tQYUVvFPdAHfd3sUVrVgDc2c4JEIiLqOhKhnb9ltFotKioq0KNHD/2yrKws2NjYwNXVtdMCiqGiogJKpRIajQYODg5ixzErZ/M1mLTyIBq1Aj6JDcUjA3uKHYmIiIxEW35/t+sIUG1tLerr6/Xl5/Lly1i6dCnS0tKMvvyQuPp7KjEvpg8AYOEPZ5FfXityIiIiMkXtKkATJ07EunXrAADl5eWIiorCxx9/jEmTJmHVqlWdGpDMzx+H+2OgtwqVdU14+buT0Ol4KoyIiDpXuwpQcnIyhg0bBgD47rvv4ObmhsuXL2PdunVYtmxZpwYk82Mhk2LJE2GwtpThYPoVrEvMEjsSERGZmHYVoJqaGtjb2wMAfvnlF0yePBlSqRT33HMPLl++3KkByTz5Odvi9QcDAQDx288jvbhK5ERERGRK2lWAAgICsGXLFuTk5GDnzp0YPXo0AKC4uJgXDVOn+cM9PhjW2xn1TTq89E0KmrQ6sSMREZGJaFcBWrhwIebPnw9fX19ERkYiOjoaQPPRoIEDB3ZqQDJfEokEHz0WCgcrC5zM1WDlngyxIxERkYlo923whYWFKCgoQGhoKKTS5h519OhRODg4IDAwsFNDdjfeBm9YfkjJw583pMBCKsGm54dgQE+V2JGIiMgAdflt8ADg7u6OgQMHIj8/X/9k+MjISKMvP2R4JoR6YvwADzTpBMR9cxJ1jVqxIxERkZFrVwHS6XRYvHgxlEolfHx84OPjA5VKhXfffRc6Ha/ToM4lkUjw3sRguNgrkF5chY92pokdiYiIjFy7CtAbb7yBFStW4P3338eJEydw4sQJ/O1vf8Py5cvx1ltvdXZGIvSwlePDRwcAAD4/kIlD6aUiJyIiImPWrmuAPD09sXr1av1T4K/74Ycf8PzzzyMvL6/TAoqB1wAZrgWbTuPro9lwtlPg5xfvhauDldiRiIjIQHT5NUBlZWWtXusTGBiIsrKy9nwk0V1Z+FAQAt3tUVpVj7n/PYFG3hpPRETt0K4CFBoaihUrVty0fMWKFRgwYECHQxHdirVchs+mDIKdwgJHs8p4PRAREbWLRXs2+vDDDzF+/Hjs3r1bPwdQYmIicnJy8PPPP3dqQKIb+bvY4e+PD8DsL5Pxz98uYZB3D4wNdhc7FhERGZF2HQEaMWIELly4gEceeQTl5eUoLy/H5MmTcfbsWaxfv76zMxLdZGywB/7vXj8AwMvfnkRmabXIiYiIyJi0eyLE1pw8eRKDBg2CVmvc87TwImjj0KjV4ek1h3Es6yoC3e2x+fmhsJbLxI5FREQi6ZaJEInEZimTYsXTg+BsJ8f5wkq89cMZdGKfJyIiE8YCREbNzcEKy54aCKkE+C4pFxuP5YgdiYiIjAALEBm9Ib2c8dLovgCAhVvP4kyeRuRERERk6Np0F9jkyZNv+355eXlHshC1259G9MKJ7KvYnVqM2V8m4acXhkFpYyl2LCIiMlBtOgKkVCpv+/Lx8cG0adO6KivRLUmlEnz8eBjUjtbIvVqLuG9SoNPxeiAiImpdp94FZip4F5jxOpOnweRVh9DQpMPLY/pizn0BYkciIqJuwrvAyGwFeymxeEJ/AMDHv6ThUAYfmkpERDdjASKTEztYjcfCe0InAC9+fQKFmjqxIxERkYFhASKTI5FI8O7E4GsPTW3A3P8mo6GJD00lIqL/YQEik2Qtl2H1H8Jhr7DA8ctX8dqmU5wkkYiI9FiAyGT5OttixZRBkEkl2JSch+W/posdiYiIDAQLEJm0EX1csHhi80XRS3ZdwA8peSInIiIiQ8ACRCZvSpQPZg33BwC8/O0pHMsqEzkRERGJjQWIzMJrYwMxpr8bGrQ6zFp3HJml1WJHIiIiEbEAkVmQSiVYGjsQoT2VuFrTiJlrj+FqdYPYsYiISCQsQGQ2rOUyrJkeAS+VNTJLq/HH9Umob9KKHYuIiETAAkRmxdXeCl88Mxj2CgsczSrDa9+f5u3xRERmiAWIzE5fd3t89ofm2+M3n8jDpwkXxY5ERETdjAWIzNKw3i54b1IwAGDp7ovYfCJX5ERERNSdWIDIbD0V6Y0/jmi+Pf6V707hyKUrIiciIqLuwgJEZu3VMYEYF+yORq2AWeuTcKmkSuxIRETUDViAyKxJpRJ8EhuGMLUKmtrm2+PLeHs8EZHJYwEis2dlKcOaaRHo2cMaWVdqMGPtMVTVN4kdi4iIuhALEBEAF3sF/v3MYKhsLHEypxwz1x5DbQPnCCIiMlUsQETX9Hazx/qZUc1zBGWW4Y9fcqJEIiJTxQJE9DshPZX494zBsLaU4bcLJXjhvyfQqNWJHYuIiDoZCxDRDSJ8HfGv6RGQW0jxy7kizP/2JLQ6zhZNRGRKWICIWjE0wBmrpgyChVSCH1Ly8cZmPjKDiMiUsAAR3cKofm5Y+mQYpBJgw7EcLN52jiWIiMhEiF6AVq5cCV9fX1hZWSEqKgpHjx695bqbNm1CREQEVCoVbG1tERYWhvXr17dYp6qqCnPnzkXPnj1hbW2NoKAgrF69uquHQSbqoQGe+ODRAQCAfx/Mwse/XBA5ERERdQZRC9DGjRsRFxeHRYsWITk5GaGhoRgzZgyKi4tbXd/R0RFvvPEGEhMTcerUKcyYMQMzZszAzp079evExcVhx44d+PLLL5Gamop58+Zh7ty52Lp1a3cNi0zM4xFqvDuxPwBgxZ50rNyTLnIiIiLqKIkg4jH9qKgoDB48GCtWrAAA6HQ6qNVqvPDCC3jttdfu6jMGDRqE8ePH49133wUABAcHIzY2Fm+99ZZ+nfDwcIwbNw7vvfdeq59RX1+P+vp6/Z8rKiqgVquh0Wjg4ODQ3uGRifnHvgzEbz8PAHj74SA8M9RP5ERERPR7FRUVUCqVd/X7W7QjQA0NDUhKSkJMTMz/wkiliImJQWJi4h23FwQBCQkJSEtLw/Dhw/XLhwwZgq1btyIvLw+CIGDPnj24cOECRo8efcvPio+Ph1Kp1L/UanXHBkcm6Y8jeuHFUb0BAG//eA7fHMsROREREbWXaAWotLQUWq0Wbm5uLZa7ubmhsLDwlttpNBrY2dlBLpdj/PjxWL58OR544AH9+8uXL0dQUBB69uwJuVyOsWPHYuXKlS1K0o0WLFgAjUajf+Xk8Bcbte4vMb3x3LDmIz+vbjqFH1LyRE5ERETtYSF2gLayt7dHSkoKqqqqkJCQgLi4OPj7+2PkyJEAmgvQ4cOHsXXrVvj4+OC3337DnDlz4Onp2eJo0+8pFAooFIpuHAUZK4lEgtcf7IeaBi2+OpKNuG9OAgAmhnmJnIyIiNpCtALk7OwMmUyGoqKiFsuLiorg7u5+y+2kUikCAgIAAGFhYUhNTUV8fDxGjhyJ2tpavP7669i8eTPGjx8PABgwYABSUlLw97///ZYFiKgtJBIJ3p0YjLpGHb5PzsW8jSmoadDiqUhvsaMREdFdEu0UmFwuR3h4OBISEvTLdDodEhISEB0dfdefo9Pp9BcwNzY2orGxEVJpy2HJZDLodHycAXUeqVSCjx4bgD/c4w1BABZsOo1/7b8kdiwiIrpLop4Ci4uLw/Tp0xEREYHIyEgsXboU1dXVmDFjBgBg2rRp8PLyQnx8PIDmi5UjIiLQq1cv1NfX4+eff8b69euxatUqAICDgwNGjBiBl19+GdbW1vDx8cG+ffuwbt06LFmyRLRxkmmSSpuPBNkpLLF6Xwbe+ykVlXVNmBfTGxKJROx4RER0G6IWoNjYWJSUlGDhwoUoLCxEWFgYduzYob8wOjs7u8XRnOrqajz//PPIzc2FtbU1AgMD8eWXXyI2Nla/zoYNG7BgwQJMmTIFZWVl8PHxwV//+lfMnj2728dHpk8ikeC1cYGwt7LARzvT8GnCRVTVN+HN8f1YgoiIDJio8wAZqrbMI0B03dqDmXj7x3MAgCcHq/HXR0Igk7IEERF1F6OYB4jI1Dwz1A8fPTZA/+ywP284gUYtrz0jIjJELEBEnejxCDVWPD0IljIJtp0qwOz1Sahr1Iodi4iIbsACRNTJHgzxwD+nRUBhIUXC+WLM+PcxVNU3iR2LiIh+hwWIqAvc19cV/5kZCTuFBRIvXcEf/nUEmppGsWMREdE1LEBEXeQefyd89X9RUNlYIiWnHLH/TERJZf2dNyQioi7HAkTUhULVKmycFQ1nOwXOF1bi0VWHkF5cJXYsIiKzxwJE1MX6utvju9nRUDtaI7usBpM/O4hDGaVixyIiMmssQETdwNfZFpufH4pB3ipU1DVh2udH8e3xHLFjERGZLRYgom7ibKfAf5+7Bw8N8ECTTsDL353CRzvPQ6fjXKRERN2NBYioG1lZyrDsyYGYe18AAGDlngy8uOEE5woiIupmLEBE3UwqlWD+mL746LEB+gkTn15zGFeqeIcYEVF3YQEiEsnjEWqsmxkFBysLJGeXY9JnB5FeXCl2LCIis8ACRCSi6F5O2DxnKHycbJBTVotHPjuEg+m8Q4yIqKuxABGJrJeLHTY/PxQRPj1QWdeE6V8cxcZj2WLHIiIyaSxARAbA0VaOL/8vChPDPNGkE/Dq96fx/nbeIUZE1FVYgIgMhJWlDEtjw/DiqN4AgNX7MvDsf46hvKZB5GRERKaHBYjIgEgkEsQ90AefxIZCYSHFnrQSPLT8AM7kacSORkRkUliAiAzQIwN7YtPzQ+DtaIPcq7WYvOoQvjnGmaOJiDoLCxCRgervqcSPc+/FqEBXNDTp8Mr3p/Da96c4aSIRUSdgASIyYEobS6yZFoH5o/tAIgE2HMvBY6sPIaesRuxoRERGjQWIyMBJpRLMvb831s2MRA8bS5zJq8BDyw9gT1qx2NGIiIwWCxCRkRjW2wXbXhyG0J5KaGobMXPtMXyy6wJvlSciagcWICIj4qWyxjezo/GHe7whCMCnCRcxY+0xXK3mrfJERG3BAkRkZBQWMrw3KQRLngiFlaUU+y403yp/Krdc7GhEREaDBYjISE0e1BOb/tT8HLG88lo8uuoQVu3NgJanxIiI7ogFiMiIBXk6YOvcezG2vzsatQI+2HEeT685jLzyWrGjEREZNBYgIiOntLbEqj8MwgePhsBGLsORzDKMXfobtp7MFzsaEZHBYgEiMgESiQSxg73x04vDEKpWobKuCS9+fQJ/2ZiCirpGseMRERkcFiAiE+LnbIvvZkfjxVG9IZUAm0/kYdzS/TiWVSZ2NCIig8ICRGRiLGVSxD3QB9/Ojoba0Rp55bWI/Uci/r4zDY1andjxiIgMAgsQkYkK93HEzy8Ow+RBXtAJwIo96Xhs1SFkllaLHY2ISHQsQEQmzN7KEkueCMOKpwdCaW2Jk7kaPPjpfnx9NBuCwNvlich8sQARmYGHBnhix7xhGNLLCbWNWizYdBrP/PsYcq/yoapEZJ5YgIjMhIfSGl8+G4XXHwyE3KJ5BunRn/yGtQczOXkiEZkdFiAiMyKVSjBreC9s//MwDPbtgZoGLd7+8RweX30IF4sqxY5HRNRtWICIzFAvFztsnBWNdycFw05hgeTscoxfdgCf7r6IhibeKUZEpo8FiMhMSaUSTL3HB7/8ZThGBbqiQavDJ7sv4OHlB3Ai+6rY8YiIuhQLEJGZ81RZ41/TI7DsqYFwspUjragSk1cdwuIfz6GmoUnseEREXYIFiIggkUgwIdQTu+JGYPJALwgC8MXBTIz+5Dfsv1gidjwiok7HAkREeo62ciyJDcPaGYPhpbJG7tVaTP38KOK+SUFJZb3Y8YiIOg0LEBHdZGRfV+z8y3A8M8QXEgmwKTkP9/99Lz4/kMnHaRCRSZAInA72JhUVFVAqldBoNHBwcBA7DpGoTmRfxaKtZ3EqVwMA6O1qh3cm9MeQAGeRkxERtdSW398sQK1gASJqSacT8M3xHHy4Mw1l1Q0AgAdD3PHG+CB4qaxFTkdE1IwFqINYgIhap6lpxCe7L2BdYhZ0AmBlKcXzIwMwa7g/rCxlYscjIjPHAtRBLEBEt5daUIFFW8/iaGYZAEDtaI23xgfhgSA3SCQSkdMRkbliAeogFiCiOxMEAT+eKsDffkpFYUUdAGB4HxcsejgIvVzsRE5HROaIBaiDWICI7l51fRNW7knHv/ZnokGrg4VUgqnRPnjh/t5wtJWLHY+IzAgLUAexABG1XVZpNRZvO4dfzxcDAOwVFvjjCH/MvNcPNnILkdMRkTlgAeogFiCi9tt/sQTvbz+Ps/kVAABXewXmxfTBExE9YSHj1GNE1HVYgDqIBYioY3Q6AT+eysdHO9OQe7UWAODvYotXxgRiTH9eKE1EXYMFqINYgIg6R32TFv89ko3lv6br5w8a6K3CgnH9EOnnKHI6IjI1LEAdxAJE1Lkq6xrxz98u4V/7M1HbqAUAxPRzxStjA9HHzV7kdERkKliAOogFiKhrFFfUYWnCRWw8lgOtToBUAkwe1BMv3t8b3k42YscjIiPHAtRBLEBEXSujpAp/35mG7WcKAQAyqQSTB3ph7v0B8HGyFTkdERkrFqAOYgEi6h7J2VexdPdF/HahBEBzEZoU1lyE/JxZhIiobViAOogFiKh7JWdfxbKEi9ib1lyEpBLoi5A/Z5UmorvEAtRBLEBE4kjJKceyhIv6yRSlEmBCqCfm3t8bAa4sQkR0eyxAHcQCRCSuU7nNRWh3anMRkkiAhwd44sVRAQhw5V1jRNQ6FqAOYgEiMgxn8jT4NOEidp0rAtBchMb2d8es4f4Y6N1D5HREZGhYgDqIBYjIsJzJ02BZwkX8cq0IAUCkryNmDffH/YGukEo5szQRsQB1GAsQkWFKK6zEP3+7hK0n89Cobf5PVy8XW8wa7o9JA72gsJCJnJCIxMQC1EEsQESGrVBTh38fysR/D2ejsr4JAOBir8AzQ3zxhygfKG0sRU5IRGJoy+9v0R/NvHLlSvj6+sLKygpRUVE4evToLdfdtGkTIiIioFKpYGtri7CwMKxfv/6m9VJTUzFhwgQolUrY2tpi8ODByM7O7sphEFE3cldaYcG4fji04H688WA/eCitUFJZj492piH6/QS88+NZ5F6tETsmERkwUY8Abdy4EdOmTcPq1asRFRWFpUuX4ttvv0VaWhpcXV1vWn/v3r24evUqAgMDIZfLsW3bNrz00kv46aefMGbMGABARkYGIiMj8eyzz+Kpp56Cg4MDzp49i3vuuafVz2wNjwARGZdGrQ4/nszHP3+7hPOFlQCaJ1UcH+KB6UN8MchbxSfQE5kBozkFFhUVhcGDB2PFihUAAJ1OB7VajRdeeAGvvfbaXX3GoEGDMH78eLz77rsAgCeffBKWlpatHhm6lfr6etTX1+v/XFFRAbVazQJEZGQEQcD+i6X452+XcCC9VL882MsB06J9MSHUE1aWvE6IyFQZxSmwhoYGJCUlISYm5n9hpFLExMQgMTHxjtsLgoCEhASkpaVh+PDhAJoL1E8//YQ+ffpgzJgxcHV1RVRUFLZs2XLbz4qPj4dSqdS/1Gp1h8ZGROKQSCQY3scFX/5fFLa9cC8eD+8JuYUUZ/Iq8Mp3p3BPfALif05FThlPjxGZO9GOAOXn58PLywuHDh1CdHS0fvkrr7yCffv24ciRI61up9Fo4OXlhfr6eshkMnz22WeYOXMmAKCwsBAeHh6wsbHBe++9h/vuuw87duzA66+/jj179mDEiBGtfiaPABGZrqvVDdh4PAdfHr6M3Ku1AJrnE7q/ryumDfHFsABn3kZPZCLacgTIopsydRp7e3ukpKSgqqoKCQkJiIuLg7+/P0aOHAmdTgcAmDhxIv7yl78AAMLCwnDo0CGsXr36lgVIoVBAoVB02xiIqPv0sJVj9oheeG6YP/acL8Z/ErOw/2IpEs4XI+F8MXydbDA12hePhfeE0pp3jxGZC9EKkLOzM2QyGYqKilosLyoqgru7+y23k0qlCAgIANBcblJTUxEfH4+RI0fC2dkZFhYWCAoKarFNv379cODAgc4fBBEZDZlUgpggN8QEueFSSRXWH76M747nIutKDd7ddg5/35mGCaGeeGKwmhdNE5kB0a4BksvlCA8PR0JCgn6ZTqdDQkJCi1Nid6LT6fSnr+RyOQYPHoy0tLQW61y4cAE+Pj6dE5yIjJ6/ix0WPdwfh18fhb8+Eoy+bvaobdRi4/EcPLrqEEZ/8hv+tf8SrlTV3/nDiMgoiXoKLC4uDtOnT0dERAQiIyOxdOlSVFdXY8aMGQCAadOmwcvLC/Hx8QCaL1aOiIhAr169UF9fj59//hnr16/HqlWr9J/58ssvIzY2FsOHD9dfA/Tjjz9i7969YgyRiAyYrcICU6J88HSkN45mlmHj8Rz8fLoAF4ur8N5Pqfhgx3nE9HND7GA1hvV2gYzXChGZDFELUGxsLEpKSrBw4UIUFhYiLCwMO3bsgJubGwAgOzsbUun/DlJVV1fj+eefR25uLqytrREYGIgvv/wSsbGx+nUeeeQRrF69GvHx8XjxxRfRt29ffP/997j33nu7fXxEZBwkEgmi/J0Q5e+Etyf0x9aUfHxzPAencjXYfqYQ288UwlNphcfCe+LxCDXUjjZiRyaiDuKjMFrBiRCJCADO5Vfgm+M52HwiD5raRgDNd5AN7eWMJwarMTrIjfMKERkQo5kI0VCxABHR79U1avHLuSJ8cyynxQSLdgoLjA12xyMDvXCPvxNPkRGJjAWog1iAiOhWcspq8O3xHHyfnIe88lr9cjcHBSaEemLSQC8EeTjwLjIiEbAAdRALEBHdiU4n4Pjlq9iSkoefThXoT5EBQB83O0wa6IWJYV7wUlmLmJLIvLAAdRALEBG1RX2TFnvTSvBDSh52pxajoUmnfy/SzxGTwrzwYIg7VDZyEVMSmT4WoA5iASKi9tLUNmLnmUJsPpGHw5lXcP2/sBZSCYYGOGN8iAdG93djGSLqAixAHcQCRESdoUBTi60p+dh8Ig/nCyv1yy2kEkT3crpWhtzhaMsyRNQZWIA6iAWIiDpbRkkVfj5VgJ9OF7QoQzKpBNH+TngwxANj+rvByY7PJSRqLxagDmIBIqKudKmkCtvPFOKnUwU4V1ChXy6TSnCPvyPGBXtgdJAbXB2sRExJZHxYgDqIBYiIuktWaTV+PlOAn08X4ExeRYv3QtUqPNDPFQ8EuaOPmx1vrSe6AxagDmIBIiIxXL5SjZ9PF2LHmQKczNW0eE/taI0H+rkjJsgVg30dYSkT7VnWRAaLBaiDWICISGxFFXVISC3G7tQiHEgvbXFrvdLaEvf1dUFMkBtG9HGBvZWliEmJDAcLUAexABGRIamub8L+i6XYda4Iv54vwtWa/026aCmT4B5/J4zo44KRfV3Qy4Wnysh8sQB1EAsQERkqrU5AcvZV7DpXhF3nipBZWt3ifS+VNUb2dcGIPi4YEuAMO4WFSEmJuh8LUAexABGRsUgvrsLetGLsu1CCI5fK0KD936kyS5kEET6OGNnXBSP7uvJCajJ5LEAdxAJERMaopqEJhy9dwd60EuxNK0F2WU2L9z2UVhjRxwX39nbGkF7OnICRTA4LUAexABGRsRMEAVlXavRHhxIzrqD+dxdSA0CQhwOGBjhhaIAzIv0cYSPn6TIybixAHcQCRESmpq5Ri8OXrmDfhRIcSr+CtKLKFu9byiQYqO6BoQHOGBrghFC1irfak9FhAeogFiAiMnUllfU4lFGKg+mlOJh+BXnltS3et5XLEOnniKEBzojyc0I/D3tYsBCRgWMB6iAWICIyJ4IgILusBgfTr+BgeikOZZS2uNUeAOwUFojw7YFIP0dE+TkixEsFuQULERkWFqAOYgEiInOm0wlILazAwfRSHL5UhmNZZaisa2qxjpWlFIO8rxciJwz0VsHKUiZSYqJmLEAdxAJERPQ/Wp2A1IIKHM0sa35llaGsuqHFOpYyCUJ7qjDYzxHh3j0wyKcH7zKjbscC1EEsQEREtyYIAtKLq3Aks6z5dekKiivrb1rPz9kWg7x7INyn+dXb1Q5SKechoq7DAtRBLEBERHfv+jVERzLLkHz5KpIuX8XF4qqb1rO3ssBA7x4Y5K1CuE8PhKlVfI4ZdSoWoA5iASIi6hhNTSOSc67qC1FKTjlqGrQt1pFIgAAXO4SqVQjtqUSoWoVAdwdeXE3txgLUQSxARESdq0mrQ1pRpb4QJWVfRU5Z7U3ryWVS9PN0QNi1QhSqVsHPyZanzuiusAB1EAsQEVHXK6msx6nccpzMKcfJXA1O5paj/Ibb7wHAXmGBAWolQrxUCPZyQLCnEt6ONixFdBMWoA5iASIi6n7XryVKySnHqVwNTuaU43Se5qZHeADNpSjI0wH9PZXNpchLCX9nW07WaOZYgDqIBYiIyDA0anW4UFSJkzkanMnX4GyeBqmFlWhopRRZWUrRz6P5CFF/Twf083BAHzd7WMs5P5G5YAHqIBYgIiLD1ajVIaOkCmfyKnAmT4Oz+Rqcy69A9Q0XWQOAVAL4Otuin7sDAt3tEejhgH4e9vBSWUMi4Sk0U8MC1EEsQERExkWnE5B1pRpn8itwNk+Ds/kVSC2owJUbJmy8zl5hgUAPewS6Nx8p6utuh95u9nDgbflGjQWog1iAiIhMQ3FlHc4XVOJ8YQVSCyqRWlCBjJIqNGpb/9Xn7mCFPu726ONqhz5u9ujt1lyM7BQW3Zyc2oMFqINYgIiITFdDU/MptPOFFThfUIlzBRW4UFSJooqbZ7O+zktljd5u10qRqx0CXO3g72IHpTWPGBkSFqAOYgEiIjI/mppGXCyuxIWiKlwsrsTFoipcKKps9TEf17nYK9DLxRa9XJoL0fWfvVTWvE1fBCxAHcQCRERE15XXNOBicXMZul6KLpVUo7Ci7pbbWFlK4efcXIj8Xezg52wDXydb+DnbQmXDh8R2FRagDmIBIiKiO6msa0RmaTUySqqQUXztnyVVyCqtQYP25tv0r1PZWOrLkK+TLXydbZp/drblRdgdxALUQSxARETUXk1aHXKv1uJSaRXSi6uQWVqNzNJqZJXW3PaoEQA42crh42QDb0cbeDvZwtvRRv9nV3sFb92/AxagDmIBIiKirlDT0ISs0hpkXbleiqr1P5dWtX7L/nVWllKoe1wvR9f+6WgDtaMNvFTWsOWdam36/c2/LSIiom5iI29+hEeQ582/nCvrGpFVWoPssuuvamSX1eDylRrkl9eirlGHi8VVuFhc1epnO9rK0bOH9bWXTYufWZBuxiNAreARICIiMiSNWh3yy2tx+crvCtK1n/PKa6GpvfkhsjdytJXDS2UND6UVPFXW8FJZw1NlDQ+VFbxU1nCxUxj9nWs8AkRERGRCLGVS+DjZwsfJttX3NbWNyLtai9yrNci9WnvtVaP/Z0VdE8qqG1BW3YDTeZpbfIcE7koreCqbi5GnygruSmu4O1jBQ2kFd6UVHG3kRl+SrmMBIiIiMnJKa0sorS1bPbUGNBek3Ks1KCivQ76mFnnltcgvr0NBeS3yy2tRWFGHRq2AnLJa5JTV3vJ7LGUSuDlYwd2huRB5KK3g5mAFD6U13BwUcHOwgou9AlaWhv8AWhYgIiIiE9dckJTo76ls9f0mrQ7FlfXIL/9dOdLUolBTh8KKOhRo6lBaVY9GraA/wnSn7/t9IXJzsIKbvQKuDlZwc1DA1d4Krg4KKCzEK0osQERERGbOQia9dtrLGhG3WKfxWkkq1NSiUFN/U0EqrqxDUUU9Gpp00NQ2QlPbiAtFrV+wDQDPDPHF2xP6d82A7gILEBEREd2RpUwKr2sXT9+KIAjQ1DaiuLIeRRV1KK6oR1Fl8z+vF6SiijoUV9bD1UHRjelvxgJEREREnUIikUBlI4fKRo4+bva3XE8QBDTpxL0JnQWIiIiIupVEIoGlTNy7yaSifjsRERGRCFiAiIiIyOywABEREZHZYQEiIiIis8MCRERERGaHBYiIiIjMDgsQERERmR0WICIiIjI7LEBERERkdliAiIiIyOywABEREZHZYQEiIiIis8MCRERERGaHT4NvhSAIAICKigqRkxAREdHduv57+/rv8dthAWpFZWUlAECtVouchIiIiNqqsrISSqXytutIhLupSWZGp9MhPz8f9vb2kEgknfrZFRUVUKvVyMnJgYODQ6d+tqEwhzECHKep4ThNhzmMEeA4WyMIAiorK+Hp6Qmp9PZX+fAIUCukUil69uzZpd/h4OBg0v+DBcxjjADHaWo4TtNhDmMEOM4b3enIz3W8CJqIiIjMDgsQERERmR0WoG6mUCiwaNEiKBQKsaN0GXMYI8BxmhqO03SYwxgBjrOjeBE0ERERmR0eASIiIiKzwwJEREREZocFiIiIiMwOCxARERGZHRagbrRy5Ur4+vrCysoKUVFROHr0qNiROtXbb78NiUTS4hUYGCh2rA777bff8PDDD8PT0xMSiQRbtmxp8b4gCFi4cCE8PDxgbW2NmJgYXLx4UZywHXCncT7zzDM37d+xY8eKE7ad4uPjMXjwYNjb28PV1RWTJk1CWlpai3Xq6uowZ84cODk5wc7ODo8++iiKiopEStw+dzPOkSNH3rQ/Z8+eLVLi9lm1ahUGDBignyAvOjoa27dv179vCvsSuPM4TWFf3uj999+HRCLBvHnz9Ms6e3+yAHWTjRs3Ii4uDosWLUJycjJCQ0MxZswYFBcXix2tU/Xv3x8FBQX614EDB8SO1GHV1dUIDQ3FypUrW33/ww8/xLJly7B69WocOXIEtra2GDNmDOrq6ro5acfcaZwAMHbs2Bb79+uvv+7GhB23b98+zJkzB4cPH8auXbvQ2NiI0aNHo7q6Wr/OX/7yF/z444/49ttvsW/fPuTn52Py5Mkipm67uxknADz33HMt9ueHH34oUuL26dmzJ95//30kJSXh+PHjuP/++zFx4kScPXsWgGnsS+DO4wSMf1/+3rFjx/CPf/wDAwYMaLG80/enQN0iMjJSmDNnjv7PWq1W8PT0FOLj40VM1bkWLVokhIaGih2jSwEQNm/erP+zTqcT3N3dhY8++ki/rLy8XFAoFMLXX38tQsLOceM4BUEQpk+fLkycOFGUPF2luLhYACDs27dPEITmfWdpaSl8++23+nVSU1MFAEJiYqJYMTvsxnEKgiCMGDFC+POf/yxeqC7So0cP4V//+pfJ7svrro9TEExrX1ZWVgq9e/cWdu3a1WJcXbE/eQSoGzQ0NCApKQkxMTH6ZVKpFDExMUhMTBQxWee7ePEiPD094e/vjylTpiA7O1vsSF0qMzMThYWFLfatUqlEVFSUye1bANi7dy9cXV3Rt29f/OlPf8KVK1fEjtQhGo0GAODo6AgASEpKQmNjY4v9GRgYCG9vb6PenzeO87qvvvoKzs7OCA4OxoIFC1BTUyNGvE6h1WqxYcMGVFdXIzo62mT35Y3jvM5U9uWcOXMwfvz4FvsN6Jp/N/kw1G5QWloKrVYLNze3Fsvd3Nxw/vx5kVJ1vqioKKxduxZ9+/ZFQUEB3nnnHQwbNgxnzpyBvb292PG6RGFhIQC0um+vv2cqxo4di8mTJ8PPzw8ZGRl4/fXXMW7cOCQmJkImk4kdr810Oh3mzZuHoUOHIjg4GEDz/pTL5VCpVC3WNeb92do4AeDpp5+Gj48PPD09cerUKbz66qtIS0vDpk2bREzbdqdPn0Z0dDTq6upgZ2eHzZs3IygoCCkpKSa1L281TsB09uWGDRuQnJyMY8eO3fReV/y7yQJEnWbcuHH6nwcMGICoqCj4+Pjgm2++wbPPPitiMuoMTz75pP7nkJAQDBgwAL169cLevXsxatQoEZO1z5w5c3DmzBmTuE7tdm41zlmzZul/DgkJgYeHB0aNGoWMjAz06tWru2O2W9++fZGSkgKNRoPvvvsO06dPx759+8SO1eluNc6goCCT2Jc5OTn485//jF27dsHKyqpbvpOnwLqBs7MzZDLZTVerFxUVwd3dXaRUXU+lUqFPnz5IT08XO0qXub7/zG3fAoC/vz+cnZ2Ncv/OnTsX27Ztw549e9CzZ0/9cnd3dzQ0NKC8vLzF+sa6P281ztZERUUBgNHtT7lcjoCAAISHhyM+Ph6hoaH49NNPTW5f3mqcrTHGfZmUlITi4mIMGjQIFhYWsLCwwL59+7Bs2TJYWFjAzc2t0/cnC1A3kMvlCA8PR0JCgn6ZTqdDQkJCi3O4pqaqqgoZGRnw8PAQO0qX8fPzg7u7e4t9W1FRgSNHjpj0vgWA3NxcXLlyxaj2ryAImDt3LjZv3oxff/0Vfn5+Ld4PDw+HpaVli/2ZlpaG7Oxso9qfdxpna1JSUgDAqPZna3Q6Herr601mX97K9XG2xhj35ahRo3D69GmkpKToXxEREZgyZYr+507fnx2/ZpvuxoYNGwSFQiGsXbtWOHfunDBr1ixBpVIJhYWFYkfrNC+99JKwd+9eITMzUzh48KAQExMjODs7C8XFxWJH65DKykrhxIkTwokTJwQAwpIlS4QTJ04Ily9fFgRBEN5//31BpVIJP/zwg3Dq1Clh4sSJgp+fn1BbWyty8ra53TgrKyuF+fPnC4mJiUJmZqawe/duYdCgQULv3r2Furo6saPftT/96U+CUqkU9u7dKxQUFOhfNTU1+nVmz54teHt7C7/++qtw/PhxITo6WoiOjhYxddvdaZzp6enC4sWLhePHjwuZmZnCDz/8IPj7+wvDhw8XOXnbvPbaa8K+ffuEzMxM4dSpU8Jrr70mSCQS4ZdffhEEwTT2pSDcfpymsi9bc+PdbZ29P1mAutHy5csFb29vQS6XC5GRkcLhw4fFjtSpYmNjBQ8PD0EulwteXl5CbGyskJ6eLnasDtuzZ48A4KbX9OnTBUFovhX+rbfeEtzc3ASFQiGMGjVKSEtLEzd0O9xunDU1NcLo0aMFFxcXwdLSUvDx8RGee+45oyvwrY0PgPDvf/9bv05tba3w/PPPCz169BBsbGyERx55RCgoKBAvdDvcaZzZ2dnC8OHDBUdHR0GhUAgBAQHCyy+/LGg0GnGDt9HMmTMFHx8fQS6XCy4uLsKoUaP05UcQTGNfCsLtx2kq+7I1Nxagzt6fEkEQhPYdOyIiIiIyTrwGiIiIiMwOCxARERGZHRYgIiIiMjssQERERGR2WICIiIjI7LAAERERkdlhASIiIiKzwwJEREREZocFiIgIgK+vL5YuXSp2DCLqJixARNTtnnnmGUyaNAkAMHLkSMybN6/bvnvt2rVQqVQ3LT927BhmzZrVbTmISFwWYgcgIuoMDQ0NkMvl7d7excWlE9MQkaHjESAiEs0zzzyDffv24dNPP4VEIoFEIkFWVhYA4MyZMxg3bhzs7Ozg5uaGqVOnorS0VL/tyJEjMXfuXMybNw/Ozs4YM2YMAGDJkiUICQmBra0t1Go1nn/+eVRVVQEA9u7dixkzZkCj0ei/7+233wZw8ymw7OxsTJw4EXZ2dnBwcMATTzyBoqIi/ftvv/02wsLCsH79evj6+kKpVOLJJ59EZWWlfp3vvvsOISEhsLa2hpOTE2JiYlBdXd1Ff5tE1BYsQEQkmk8//RTR0dF47rnnUFBQgIKCAqjVapSXl+P+++/HwIEDcfz4cezYsQNFRUV44oknWmz/n//8B3K5HAcPHsTq1asBAFKpFMuWLcPZs2fxn//8B7/++iteeeUVAMCQIUOwdOlSODg46L9v/vz5N+XS6XSYOHEiysrKsG/fPuzatQuXLl1CbGxsi/UyMjKwZcsWbNu2Ddu2bcO+ffvw/vvvAwAKCgrw1FNPYebMmUhNTcXevXsxefJk8PnTRIaBp8CISDRKpRJyuRw2NjZwd3fXL1+xYgUGDhyIv/3tb/plX3zxBdRqNS5cuIA+ffoAAHr37o0PP/ywxWf+/noiX19fvPfee5g9ezY+++wzyOVyKJVKSCSSFt93o4SEBJw+fRqZmZlQq9UAgHXr1qF///44duwYBg8eDKC5KK1duxb29vYAgKlTpyIhIQF//etfUVBQgKamJkyePBk+Pj4AgJCQkA78bRFRZ+IRICIyOCdPnsSePXtgZ2enfwUGBgJoPupyXXh4+E3b7t69G6NGjYKXlxfs7e0xdepUXLlyBTU1NXf9/ampqVCr1fryAwBBQUFQqVRITU3VL/P19dWXHwDw8PBAcXExACA0NBSjRo1CSEgIHn/8caxZswZXr169+78EIupSLEBEZHCqqqrw8MMPIyUlpcXr4sWLGD58uH49W1vbFttlZWXhoYcewoABA/D9998jKSkJK1euBNB8kXRns7S0bPFniUQCnU4HAJDJZNi1axe2b9+OoKAgLF++HH379kVmZman5yCitmMBIiJRyeVyaLXaFssGDRqEs2fPwtfXFwEBAS1eN5ae30tKSoJOp8PHH3+Me+65B3369EF+fv4dv+9G/fr1Q05ODnJycvTLzp07h/LycgQFBd312CQSCYYOHYp33nkHJ06cgFwux+bNm+96eyLqOixARCQqX19fHDlyBFlZWSgtLYVOp8OcOXNQVlaGp556CseOHUNGRgZ27tyJGTNm3La8BAQEoLGxEcuXL8elS5ewfv16/cXRv/++qqoqJCQkoLS0tNVTYzExMQgJCcGUKVOQnJyMo0ePYtq0aRgxYgQiIiLualxHjhzB3/72Nxw/fhzZ2dnYtGkTSkpK0K9fv7b9BRFRl2ABIiJRzZ8/HzKZDEFBQXBxcUF2djY8PT1x8OBBaLVajB49GiEhIZg3bx5UKhWk0lv/Zys0NBRLlizBBx98gODgYHz11VeIj49vsc6QIUMwe/ZsxMbGwsXF5aaLqIHmIzc//PADevTogeHDhyMmJgb+/v7YuHHjXY/LwcEBv/32Gx588EH06dMHb775Jj7++GOMGzfu7v9yiKjLSATek0lERERmhkeAiIiIyOywABEREZHZYQEiIiIis8MCRERERGaHBYiIiIjMDgsQERERmR0WICIiIjI7LEBERERkdliAiIiIyOywABEREZHZYQEiIiIis/P/TLav0RbZBxQAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "epochs = 40\n",
        "learning_rate = 0.001\n",
        "w_offline, cost_list_offline = fit(X_train, y_train, epochs = epochs, learning_rate = learning_rate)\n",
        "print(f\"Weights: {w_offline}\")\n",
        "plt.plot(cost_list_offline)\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"Loss\")"
      ],
      "id": "zFjUcbNGlVUC"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4-D3TNC1lVUC"
      },
      "source": [
        "# Mini batch Gradient Descent\n",
        "In mini batch gradient descent, we create batches of the training data and use one batch at a time. After one forward pass using one batch, the weight gets update. That means, we update the weights more frequently than offline learning."
      ],
      "id": "4-D3TNC1lVUC"
    },
    {
      "cell_type": "code",
      "execution_count": 93,
      "metadata": {
        "id": "rmUz3O0ulVUC"
      },
      "outputs": [],
      "source": [
        "def create_mini_batches(X, y, batch_size):\n",
        "    mini_batches = []\n",
        "    data = np.hstack((X, y))\n",
        "    np.random.shuffle(data)\n",
        "    n_minibatches = data.shape[0] // batch_size\n",
        "    i = 0\n",
        "\n",
        "    for i in range(n_minibatches):\n",
        "        mini_batch = data[i * batch_size:(i + 1)*batch_size, :]\n",
        "        X_mini = mini_batch[:, :-1]\n",
        "        Y_mini = mini_batch[:, -1].reshape((-1, 1))\n",
        "        mini_batches.append((X_mini, Y_mini))\n",
        "    if data.shape[0] % batch_size != 0:\n",
        "        mini_batch = data[i * batch_size:data.shape[0]]\n",
        "        X_mini = mini_batch[:, :-1]\n",
        "        Y_mini = mini_batch[:, -1].reshape((-1, 1))\n",
        "        mini_batches.append((X_mini, Y_mini))\n",
        "    return mini_batches"
      ],
      "id": "rmUz3O0ulVUC"
    },
    {
      "cell_type": "code",
      "execution_count": 122,
      "metadata": {
        "id": "W4uxmh5KlVUC"
      },
      "outputs": [],
      "source": [
        "def fit_mini(X, y, batch_size = 10, epochs=10, learning_rate=0.00001):\n",
        "    N = X.shape[0]\n",
        "    w = np.ones((1, X.shape[1]))\n",
        "    cost_list = []\n",
        "    number_of_batch = N // batch_size\n",
        "    old_cost = 10\n",
        "\n",
        "    for k in range(epochs):\n",
        "        mini_batches = create_mini_batches(X, y.reshape(len(y),1), batch_size)\n",
        "        for mini_batch in mini_batches:\n",
        "            X_mini, y_mini = mini_batch\n",
        "            y_proba = probability(w, X_mini)\n",
        "            update = learning_rate * gradient_compute(X_mini, np.squeeze(y_mini), y_proba)\n",
        "            w = w - update\n",
        "            #print(update)\n",
        "\n",
        "            loss = 0\n",
        "            total_cost = 0\n",
        "            for i in range(len(y_mini)):\n",
        "                loss += cost(y_mini[i], y_proba[i])\n",
        "\n",
        "            total_cost = loss / len(y_mini)\n",
        "            cost_list.append(total_cost)\n",
        "    return w, cost_list"
      ],
      "id": "W4uxmh5KlVUC"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O4tRp5lelVUC"
      },
      "source": [
        "## Training"
      ],
      "id": "O4tRp5lelVUC"
    },
    {
      "cell_type": "code",
      "source": [
        "#Last weights\n",
        "print(f\"Weights: {w_offline}\")\n",
        "\n",
        "#Last element\n",
        "print(cost_list_offline[-1:])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XWToXNua5nHD",
        "outputId": "fb434013-a909-4011-8a45-298bbcf731cd"
      },
      "id": "XWToXNua5nHD",
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Weights: [[ 0.54462583  0.64393505  0.74900803  0.40164323  1.09063782  0.65710503\n",
            "  -0.01551585  0.77141872]]\n",
            "[0.34616596544554684]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 154,
      "metadata": {
        "id": "7Tg0O2zAlVUC",
        "outputId": "e5a4ec34-ab98-423c-c0cf-259c6891f5ac",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Weights: [[0.59885262 0.66391665 0.77448373 0.42632469 1.1163704  0.67980351\n",
            "  0.02030957 0.7871632 ]]\n",
            "[array([0.29720699])]\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Loss')"
            ]
          },
          "metadata": {},
          "execution_count": 154
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "epochs = 30\n",
        "learning_rate = 0.001\n",
        "w_mini, cost_list_mini = fit_mini(X_train, y_train, batch_size = 128, epochs = epochs, learning_rate = learning_rate)\n",
        "print(f\"Weights: {w_mini}\")\n",
        "#Last cost\n",
        "print(cost_list_mini[-1:])\n",
        "\n",
        "plt.plot(cost_list_mini)\n",
        "plt.xlabel(\"Iterations\")\n",
        "plt.ylabel(\"Loss\")"
      ],
      "id": "7Tg0O2zAlVUC"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tHWs6zYelVUC"
      },
      "source": [
        "# Evaluation Metrics\n",
        "\n",
        "The following evaluation metrics are used to evaluate the LDA model:\n",
        "* accuracy = (TN + TP)/ N\n",
        "* sensitivity = TP / (TP + FN)\n",
        "* specificity = TN / (TN + FP)\n",
        "* precision = TP / (TP + FP)\n",
        "* f1-score = $2*\\frac{precision * sensitivity} {precision + sensitivity}$\n",
        "* log loss = $- \\frac{1}{N} * \\sum_{i}^{N} [y_i*ln(p_i) + (1-y_i)*ln(1-p_i)]$\n",
        "\n",
        "Here,\n",
        "\n",
        "TP= True Positive\\\n",
        "TN= True Negative\\\n",
        "FP= False Positive\\\n",
        "FN= False Negative\\\n",
        "$y_i$ = ground truth of instance i\\\n",
        "$p_i$ = probability of instance of i"
      ],
      "id": "tHWs6zYelVUC"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "KJusWRrClVUD"
      },
      "outputs": [],
      "source": [
        "def compute_confusion_matrix(true, pred):\n",
        "    '''Computes a confusion matrix using numpy.'''\n",
        "\n",
        "    K = len(np.unique(true)) # Number of classes\n",
        "    result = np.zeros((K, K))\n",
        "\n",
        "    for i in range(len(true)):\n",
        "        result[true[i]][pred[i]] += 1\n",
        "\n",
        "    return result"
      ],
      "id": "KJusWRrClVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "j_5wohsrlVUD"
      },
      "outputs": [],
      "source": [
        "def accuracy(conf_matrix):\n",
        "    tn, fp, fn, tp = conf_matrix.ravel()\n",
        "    return (tp+tn)/(tp+tn+fp+fn)"
      ],
      "id": "j_5wohsrlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "tla6lqKulVUD"
      },
      "outputs": [],
      "source": [
        "def sensitivity(conf_matrix):\n",
        "    tn, fp, fn, tp = conf_matrix.ravel()\n",
        "    return tp/(tp+fn)"
      ],
      "id": "tla6lqKulVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5JU47l5KlVUD"
      },
      "outputs": [],
      "source": [
        "def specificity(conf_matrix):\n",
        "    tn, fp, fn, tp = conf_matrix.ravel()\n",
        "    return tn/(tn+fp)"
      ],
      "id": "5JU47l5KlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TqqRNVUTlVUD"
      },
      "outputs": [],
      "source": [
        "def precision(conf_matrix):\n",
        "    tn, fp, fn, tp = conf_matrix.ravel()\n",
        "    return tp/(tp+fp)"
      ],
      "id": "TqqRNVUTlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Shg8xnvSlVUD"
      },
      "outputs": [],
      "source": [
        "def f1_score(conf_matrix):\n",
        "    tn, fp, fn, tp = conf_matrix.ravel()\n",
        "    precision = tp/(tp+fp)\n",
        "    recall = tp/(tp+fn)\n",
        "    f1_score = 2 * (precision * recall)/(precision + recall)\n",
        "    return f1_score"
      ],
      "id": "Shg8xnvSlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "jlqwpQr9lVUD"
      },
      "outputs": [],
      "source": [
        "def log_loss(ground_truth, y_proba):\n",
        "    log_loss = -((ground_truth * np.log(y_proba)) + ((1-ground_truth) * np.log(1-y_proba))).mean()\n",
        "    return log_loss"
      ],
      "id": "jlqwpQr9lVUD"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UynF04LulVUD"
      },
      "source": [
        "# Evaluating Offline Model"
      ],
      "id": "UynF04LulVUD"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MH_bIS27lVUD"
      },
      "source": [
        "## Evaluation metrics for train set"
      ],
      "id": "MH_bIS27lVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "MtRE-IlBlVUD",
        "outputId": "56d89b90-0393-4ae5-ced5-d23e94c3d7e4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[298.,  62.],\n",
              "       [ 53., 307.]])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ],
      "source": [
        "y_train_proba = probability(w_offline, X_train)\n",
        "y_train_pred = prediction(y_train_proba)\n",
        "\n",
        "conf_matrix_train = compute_confusion_matrix(y_train, y_train_pred)\n",
        "conf_matrix_train"
      ],
      "id": "MtRE-IlBlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5aX6fDCPlVUD",
        "outputId": "dcc56200-84ba-4442-d397-19db05900e25",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8402777777777778"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ],
      "source": [
        "accuracy(conf_matrix_train)"
      ],
      "id": "5aX6fDCPlVUD"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xYb5itCklVUE",
        "outputId": "062e8aa7-9bcd-461e-be02-44c69324d4cc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8527777777777777"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ],
      "source": [
        "# Recall\n",
        "sensitivity(conf_matrix_train)"
      ],
      "id": "xYb5itCklVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1VHdLjSIlVUE",
        "outputId": "59219f54-49d7-4ac5-aec1-a03e0c81c927",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8277777777777777"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ],
      "source": [
        "# Negative recall\n",
        "specificity(conf_matrix_train)"
      ],
      "id": "1VHdLjSIlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "1644AK7KlVUE",
        "outputId": "c455c34c-9be3-4da9-bedf-365a8a4d0877",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.842249657064472"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ],
      "source": [
        "f1_score(conf_matrix_train)"
      ],
      "id": "1644AK7KlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WV3P8ImelVUE",
        "outputId": "6aa5b5d2-f6f6-4abf-b050-24cf969da6a8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3793508241902827"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ],
      "source": [
        "log_loss(y_train, y_train_proba)"
      ],
      "id": "WV3P8ImelVUE"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DNxxFpvqlVUE"
      },
      "source": [
        "## Evaluation metrics for test set"
      ],
      "id": "DNxxFpvqlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_bZ6K7mUlVUE",
        "outputId": "db41caba-4e38-4291-b440-fe454baae178"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[80., 10.],\n",
              "       [18., 72.]])"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y_test_proba = probability(w_offline, X_test)\n",
        "y_test_pred = prediction(y_test_proba)\n",
        "\n",
        "conf_matrix_test = compute_confusion_matrix(y_test, y_test_pred)\n",
        "conf_matrix_test"
      ],
      "id": "_bZ6K7mUlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gLHv3IIAlVUE",
        "outputId": "c1bd490a-638e-4955-9e52-b0d7fe6ad892"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8444444444444444"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "accuracy(conf_matrix_test)"
      ],
      "id": "gLHv3IIAlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FNJ7e8qKlVUE",
        "outputId": "ae95ccff-6884-43cb-92f7-fcbd02f07592"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sensitivity(conf_matrix_test)"
      ],
      "id": "FNJ7e8qKlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lqM8ZD2TlVUE",
        "outputId": "f3cc6416-7259-4dd6-bc79-111c43761653"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8888888888888888"
            ]
          },
          "execution_count": 47,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "specificity(conf_matrix_test)"
      ],
      "id": "lqM8ZD2TlVUE"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "YGnN74p1lVUE",
        "outputId": "bd323641-4fc2-4951-c0a0-9329c1b81f4a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8372093023255814"
            ]
          },
          "execution_count": 48,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f1_score(conf_matrix_test)"
      ],
      "id": "YGnN74p1lVUE"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rH4aI-jClVUF"
      },
      "source": [
        "# Evaluating Mini batch Gradient Descent Model"
      ],
      "id": "rH4aI-jClVUF"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3M7U_qRulVUF"
      },
      "source": [
        "## Evaluation metrics for train set"
      ],
      "id": "3M7U_qRulVUF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "m7wCHByDlVUF",
        "outputId": "b1d366f2-1252-4146-93ce-ce204e494687"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[320.,  40.],\n",
              "       [ 51., 309.]])"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y_train_proba = probability(w_mini, X_train)\n",
        "y_train_pred = prediction(y_train_proba)\n",
        "\n",
        "conf_matrix_train = compute_confusion_matrix(y_train, y_train_pred)\n",
        "conf_matrix_train"
      ],
      "id": "m7wCHByDlVUF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "V5POTVholVUF",
        "outputId": "222fd55f-49a2-417c-bf64-d84f7d2e0dfb"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8736111111111111"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "accuracy(conf_matrix_train)"
      ],
      "id": "V5POTVholVUF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gsqJUwj6lVUF",
        "outputId": "280d2844-a083-4fa5-fa70-da4b63f4f629"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8583333333333333"
            ]
          },
          "execution_count": 51,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sensitivity(conf_matrix_train)"
      ],
      "id": "gsqJUwj6lVUF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "P38piZ6YlVUF",
        "outputId": "3e5d7b0a-293c-4581-845a-d1d2e77bcda9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8888888888888888"
            ]
          },
          "execution_count": 52,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "specificity(conf_matrix_train)"
      ],
      "id": "P38piZ6YlVUF"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "5HIfLtlslVUG",
        "outputId": "4bbdcaae-a32c-4d61-a553-c68213334ab8"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8716502115655854"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f1_score(conf_matrix_train)"
      ],
      "id": "5HIfLtlslVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TflYPB0BlVUG",
        "outputId": "92752341-f1df-4430-c57b-f9b945d051e5"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.34093795760947293"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "log_loss(y_train, y_train_proba)"
      ],
      "id": "TflYPB0BlVUG"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QJFSsOWrlVUG"
      },
      "source": [
        "## Evaluation metrics for test set"
      ],
      "id": "QJFSsOWrlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "I2v03towlVUG",
        "outputId": "f99a2317-91e2-45fa-d208-9fea56f83c75"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[80., 10.],\n",
              "       [18., 72.]])"
            ]
          },
          "execution_count": 55,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "y_test_proba = probability(w_mini, X_test)\n",
        "y_test_pred = prediction(y_test_proba)\n",
        "\n",
        "conf_matrix_test = compute_confusion_matrix(y_test, y_test_pred)\n",
        "conf_matrix_test"
      ],
      "id": "I2v03towlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "0EtrNT5vlVUG",
        "outputId": "34ddc7c3-c2ef-4bb0-916a-f0f0932fd1b2"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8444444444444444"
            ]
          },
          "execution_count": 56,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "accuracy(conf_matrix_test)"
      ],
      "id": "0EtrNT5vlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WWR8dpVnlVUG",
        "outputId": "b236caa9-44c2-4f48-e077-9d36eef6ac56"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8"
            ]
          },
          "execution_count": 57,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sensitivity(conf_matrix_test)"
      ],
      "id": "WWR8dpVnlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "k8cvS7-KlVUG",
        "outputId": "4eaa4b8e-1829-44d6-b206-cf3b4e075e6b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8888888888888888"
            ]
          },
          "execution_count": 58,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "specificity(conf_matrix_test)"
      ],
      "id": "k8cvS7-KlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "_CY2dVgmlVUG",
        "outputId": "8c55feb5-70e5-4ebc-a53b-050f3e10b15b"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.8372093023255814"
            ]
          },
          "execution_count": 59,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "f1_score(conf_matrix_test)"
      ],
      "id": "_CY2dVgmlVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "K-cHrPbclVUG",
        "outputId": "40159232-d52c-4659-ce72-d57969450574"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.4085944927842661"
            ]
          },
          "execution_count": 60,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "log_loss(y_test, y_test_proba)"
      ],
      "id": "K-cHrPbclVUG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vWiTFtPslVUG",
        "outputId": "edbf19e4-5322-4af9-8e10-57a839f60650"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "0.4085944927842661"
            ]
          },
          "execution_count": 61,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "log_loss(y_test, y_test_proba)"
      ],
      "id": "vWiTFtPslVUG"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.4"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
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  "nbformat_minor": 5
}