fraud_detection.ipynb

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    "colab": {
      "name": "Fraud Detection",
      "provenance": [],
      "collapsed_sections": [],
      "toc_visible": true,
      "mount_file_id": "1YW2ptstNV8J7QwUyNwdD8as7ZCU3a0t9",
      "authorship_tag": "ABX9TyPbRj51GVpri0FcnabwwCKU"
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      "name": "python3",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IgzTKmhAodZ0"
      },
      "source": [
        "# 1) Workspace setup and data import\n",
        "\n",
        "The original data can be downloaded [here](https://www.kaggle.com/mlg-ulb/creditcardfraud)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2OvX8nWi4_-3"
      },
      "source": [
        "# General libraries\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import seaborn as sns\n",
        "\n",
        "# Logistic Regression Classifier\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "# Recursive feature elimination\n",
        "from sklearn.feature_selection import RFE, RFECV\n",
        "\n",
        "# Model Evaluation\n",
        "from sklearn.metrics import accuracy_score, classification_report, precision_score, recall_score, f1_score\n",
        "from sklearn.metrics import confusion_matrix, precision_recall_curve, roc_curve, auc, log_loss\n",
        "\n",
        "# Other Libraries\n",
        "from sklearn.model_selection import train_test_split, GridSearchCV, cross_val_score\n",
        "\n",
        "\n",
        "# from sklearn.pipeline import make_pipeline\n",
        "# from imblearn.pipeline import make_pipeline as imbalanced_make_pipeline\n",
        "# from imblearn.under_sampling import NearMiss\n",
        "# from imblearn.metrics import classification_report_imbalanced\n",
        "# import collections\n",
        "# from collections import Counter\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")"
      ],
      "execution_count": 185,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iLhwtnhf_NkA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 224
        },
        "outputId": "69b69685-5a0c-4248-b29e-5823ab665682"
      },
      "source": [
        "# Import data into pandas dataframe\n",
        "data = pd.read_csv('.../creditcard.csv')\n",
        "data.head()"
      ],
      "execution_count": 186,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Time</th>\n",
              "      <th>V1</th>\n",
              "      <th>V2</th>\n",
              "      <th>V3</th>\n",
              "      <th>V4</th>\n",
              "      <th>V5</th>\n",
              "      <th>V6</th>\n",
              "      <th>V7</th>\n",
              "      <th>V8</th>\n",
              "      <th>V9</th>\n",
              "      <th>V10</th>\n",
              "      <th>V11</th>\n",
              "      <th>V12</th>\n",
              "      <th>V13</th>\n",
              "      <th>V14</th>\n",
              "      <th>V15</th>\n",
              "      <th>V16</th>\n",
              "      <th>V17</th>\n",
              "      <th>V18</th>\n",
              "      <th>V19</th>\n",
              "      <th>V20</th>\n",
              "      <th>V21</th>\n",
              "      <th>V22</th>\n",
              "      <th>V23</th>\n",
              "      <th>V24</th>\n",
              "      <th>V25</th>\n",
              "      <th>V26</th>\n",
              "      <th>V27</th>\n",
              "      <th>V28</th>\n",
              "      <th>Amount</th>\n",
              "      <th>Class</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.0</td>\n",
              "      <td>-1.359807</td>\n",
              "      <td>-0.072781</td>\n",
              "      <td>2.536347</td>\n",
              "      <td>1.378155</td>\n",
              "      <td>-0.338321</td>\n",
              "      <td>0.462388</td>\n",
              "      <td>0.239599</td>\n",
              "      <td>0.098698</td>\n",
              "      <td>0.363787</td>\n",
              "      <td>0.090794</td>\n",
              "      <td>-0.551600</td>\n",
              "      <td>-0.617801</td>\n",
              "      <td>-0.991390</td>\n",
              "      <td>-0.311169</td>\n",
              "      <td>1.468177</td>\n",
              "      <td>-0.470401</td>\n",
              "      <td>0.207971</td>\n",
              "      <td>0.025791</td>\n",
              "      <td>0.403993</td>\n",
              "      <td>0.251412</td>\n",
              "      <td>-0.018307</td>\n",
              "      <td>0.277838</td>\n",
              "      <td>-0.110474</td>\n",
              "      <td>0.066928</td>\n",
              "      <td>0.128539</td>\n",
              "      <td>-0.189115</td>\n",
              "      <td>0.133558</td>\n",
              "      <td>-0.021053</td>\n",
              "      <td>149.62</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.0</td>\n",
              "      <td>1.191857</td>\n",
              "      <td>0.266151</td>\n",
              "      <td>0.166480</td>\n",
              "      <td>0.448154</td>\n",
              "      <td>0.060018</td>\n",
              "      <td>-0.082361</td>\n",
              "      <td>-0.078803</td>\n",
              "      <td>0.085102</td>\n",
              "      <td>-0.255425</td>\n",
              "      <td>-0.166974</td>\n",
              "      <td>1.612727</td>\n",
              "      <td>1.065235</td>\n",
              "      <td>0.489095</td>\n",
              "      <td>-0.143772</td>\n",
              "      <td>0.635558</td>\n",
              "      <td>0.463917</td>\n",
              "      <td>-0.114805</td>\n",
              "      <td>-0.183361</td>\n",
              "      <td>-0.145783</td>\n",
              "      <td>-0.069083</td>\n",
              "      <td>-0.225775</td>\n",
              "      <td>-0.638672</td>\n",
              "      <td>0.101288</td>\n",
              "      <td>-0.339846</td>\n",
              "      <td>0.167170</td>\n",
              "      <td>0.125895</td>\n",
              "      <td>-0.008983</td>\n",
              "      <td>0.014724</td>\n",
              "      <td>2.69</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>-1.358354</td>\n",
              "      <td>-1.340163</td>\n",
              "      <td>1.773209</td>\n",
              "      <td>0.379780</td>\n",
              "      <td>-0.503198</td>\n",
              "      <td>1.800499</td>\n",
              "      <td>0.791461</td>\n",
              "      <td>0.247676</td>\n",
              "      <td>-1.514654</td>\n",
              "      <td>0.207643</td>\n",
              "      <td>0.624501</td>\n",
              "      <td>0.066084</td>\n",
              "      <td>0.717293</td>\n",
              "      <td>-0.165946</td>\n",
              "      <td>2.345865</td>\n",
              "      <td>-2.890083</td>\n",
              "      <td>1.109969</td>\n",
              "      <td>-0.121359</td>\n",
              "      <td>-2.261857</td>\n",
              "      <td>0.524980</td>\n",
              "      <td>0.247998</td>\n",
              "      <td>0.771679</td>\n",
              "      <td>0.909412</td>\n",
              "      <td>-0.689281</td>\n",
              "      <td>-0.327642</td>\n",
              "      <td>-0.139097</td>\n",
              "      <td>-0.055353</td>\n",
              "      <td>-0.059752</td>\n",
              "      <td>378.66</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.966272</td>\n",
              "      <td>-0.185226</td>\n",
              "      <td>1.792993</td>\n",
              "      <td>-0.863291</td>\n",
              "      <td>-0.010309</td>\n",
              "      <td>1.247203</td>\n",
              "      <td>0.237609</td>\n",
              "      <td>0.377436</td>\n",
              "      <td>-1.387024</td>\n",
              "      <td>-0.054952</td>\n",
              "      <td>-0.226487</td>\n",
              "      <td>0.178228</td>\n",
              "      <td>0.507757</td>\n",
              "      <td>-0.287924</td>\n",
              "      <td>-0.631418</td>\n",
              "      <td>-1.059647</td>\n",
              "      <td>-0.684093</td>\n",
              "      <td>1.965775</td>\n",
              "      <td>-1.232622</td>\n",
              "      <td>-0.208038</td>\n",
              "      <td>-0.108300</td>\n",
              "      <td>0.005274</td>\n",
              "      <td>-0.190321</td>\n",
              "      <td>-1.175575</td>\n",
              "      <td>0.647376</td>\n",
              "      <td>-0.221929</td>\n",
              "      <td>0.062723</td>\n",
              "      <td>0.061458</td>\n",
              "      <td>123.50</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2.0</td>\n",
              "      <td>-1.158233</td>\n",
              "      <td>0.877737</td>\n",
              "      <td>1.548718</td>\n",
              "      <td>0.403034</td>\n",
              "      <td>-0.407193</td>\n",
              "      <td>0.095921</td>\n",
              "      <td>0.592941</td>\n",
              "      <td>-0.270533</td>\n",
              "      <td>0.817739</td>\n",
              "      <td>0.753074</td>\n",
              "      <td>-0.822843</td>\n",
              "      <td>0.538196</td>\n",
              "      <td>1.345852</td>\n",
              "      <td>-1.119670</td>\n",
              "      <td>0.175121</td>\n",
              "      <td>-0.451449</td>\n",
              "      <td>-0.237033</td>\n",
              "      <td>-0.038195</td>\n",
              "      <td>0.803487</td>\n",
              "      <td>0.408542</td>\n",
              "      <td>-0.009431</td>\n",
              "      <td>0.798278</td>\n",
              "      <td>-0.137458</td>\n",
              "      <td>0.141267</td>\n",
              "      <td>-0.206010</td>\n",
              "      <td>0.502292</td>\n",
              "      <td>0.219422</td>\n",
              "      <td>0.215153</td>\n",
              "      <td>69.99</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Time        V1        V2        V3  ...       V27       V28  Amount  Class\n",
              "0   0.0 -1.359807 -0.072781  2.536347  ...  0.133558 -0.021053  149.62      0\n",
              "1   0.0  1.191857  0.266151  0.166480  ... -0.008983  0.014724    2.69      0\n",
              "2   1.0 -1.358354 -1.340163  1.773209  ... -0.055353 -0.059752  378.66      0\n",
              "3   1.0 -0.966272 -0.185226  1.792993  ...  0.062723  0.061458  123.50      0\n",
              "4   2.0 -1.158233  0.877737  1.548718  ...  0.219422  0.215153   69.99      0\n",
              "\n",
              "[5 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 186
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "D8mof0cy0gDw"
      },
      "source": [
        "# 2) Understanding the data\n",
        "According to the documentation, the dataset contains transactions made by credit cards in September 2013, over two days, by European cardholders.\n",
        "\n",
        "The 31 columns of the dataset only contain numerical input variables, which are the result of a PCA transformation of the original dataset. Features V1, V2, … V28 are the principal components obtained with PCA, and the only features which have not been transformed with PCA are 'Time' and 'Amount'. The original features are not provided due to  confidentiality issues.\n",
        "* 'Time' contains the seconds elapsed between each transaction and the first transaction in the dataset.\n",
        "* 'Amount' is the transaction amount\n",
        "\n",
        "**Summary**:\n",
        "* There are no null values in any of the columns of the dataset.\n",
        "* Out of 284,807 transactions, 492 (0.17%) were considered to be frauds (ie, 'Class' = 1). \n",
        "* This means that the dataset is **extremely unbalanced**. This issue is further discussed in section 4."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "52gmahP70VZ0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "34f18f84-e8ec-476f-a441-24768f29dd54"
      },
      "source": [
        "data.columns"
      ],
      "execution_count": 187,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['Time', 'V1', 'V2', 'V3', 'V4', 'V5', 'V6', 'V7', 'V8', 'V9', 'V10',\n",
              "       'V11', 'V12', 'V13', 'V14', 'V15', 'V16', 'V17', 'V18', 'V19', 'V20',\n",
              "       'V21', 'V22', 'V23', 'V24', 'V25', 'V26', 'V27', 'V28', 'Amount',\n",
              "       'Class'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 187
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lraf8tnRj4ei",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "outputId": "df5f4bf9-5093-4e9d-f12d-2720920a04f8"
      },
      "source": [
        "data.describe()"
      ],
      "execution_count": 188,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Time</th>\n",
              "      <th>V1</th>\n",
              "      <th>V2</th>\n",
              "      <th>V3</th>\n",
              "      <th>V4</th>\n",
              "      <th>V5</th>\n",
              "      <th>V6</th>\n",
              "      <th>V7</th>\n",
              "      <th>V8</th>\n",
              "      <th>V9</th>\n",
              "      <th>V10</th>\n",
              "      <th>V11</th>\n",
              "      <th>V12</th>\n",
              "      <th>V13</th>\n",
              "      <th>V14</th>\n",
              "      <th>V15</th>\n",
              "      <th>V16</th>\n",
              "      <th>V17</th>\n",
              "      <th>V18</th>\n",
              "      <th>V19</th>\n",
              "      <th>V20</th>\n",
              "      <th>V21</th>\n",
              "      <th>V22</th>\n",
              "      <th>V23</th>\n",
              "      <th>V24</th>\n",
              "      <th>V25</th>\n",
              "      <th>V26</th>\n",
              "      <th>V27</th>\n",
              "      <th>V28</th>\n",
              "      <th>Amount</th>\n",
              "      <th>Class</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>284807.000000</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>2.848070e+05</td>\n",
              "      <td>284807.000000</td>\n",
              "      <td>284807.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>94813.859575</td>\n",
              "      <td>3.919560e-15</td>\n",
              "      <td>5.688174e-16</td>\n",
              "      <td>-8.769071e-15</td>\n",
              "      <td>2.782312e-15</td>\n",
              "      <td>-1.552563e-15</td>\n",
              "      <td>2.010663e-15</td>\n",
              "      <td>-1.694249e-15</td>\n",
              "      <td>-1.927028e-16</td>\n",
              "      <td>-3.137024e-15</td>\n",
              "      <td>1.768627e-15</td>\n",
              "      <td>9.170318e-16</td>\n",
              "      <td>-1.810658e-15</td>\n",
              "      <td>1.693438e-15</td>\n",
              "      <td>1.479045e-15</td>\n",
              "      <td>3.482336e-15</td>\n",
              "      <td>1.392007e-15</td>\n",
              "      <td>-7.528491e-16</td>\n",
              "      <td>4.328772e-16</td>\n",
              "      <td>9.049732e-16</td>\n",
              "      <td>5.085503e-16</td>\n",
              "      <td>1.537294e-16</td>\n",
              "      <td>7.959909e-16</td>\n",
              "      <td>5.367590e-16</td>\n",
              "      <td>4.458112e-15</td>\n",
              "      <td>1.453003e-15</td>\n",
              "      <td>1.699104e-15</td>\n",
              "      <td>-3.660161e-16</td>\n",
              "      <td>-1.206049e-16</td>\n",
              "      <td>88.349619</td>\n",
              "      <td>0.001727</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>47488.145955</td>\n",
              "      <td>1.958696e+00</td>\n",
              "      <td>1.651309e+00</td>\n",
              "      <td>1.516255e+00</td>\n",
              "      <td>1.415869e+00</td>\n",
              "      <td>1.380247e+00</td>\n",
              "      <td>1.332271e+00</td>\n",
              "      <td>1.237094e+00</td>\n",
              "      <td>1.194353e+00</td>\n",
              "      <td>1.098632e+00</td>\n",
              "      <td>1.088850e+00</td>\n",
              "      <td>1.020713e+00</td>\n",
              "      <td>9.992014e-01</td>\n",
              "      <td>9.952742e-01</td>\n",
              "      <td>9.585956e-01</td>\n",
              "      <td>9.153160e-01</td>\n",
              "      <td>8.762529e-01</td>\n",
              "      <td>8.493371e-01</td>\n",
              "      <td>8.381762e-01</td>\n",
              "      <td>8.140405e-01</td>\n",
              "      <td>7.709250e-01</td>\n",
              "      <td>7.345240e-01</td>\n",
              "      <td>7.257016e-01</td>\n",
              "      <td>6.244603e-01</td>\n",
              "      <td>6.056471e-01</td>\n",
              "      <td>5.212781e-01</td>\n",
              "      <td>4.822270e-01</td>\n",
              "      <td>4.036325e-01</td>\n",
              "      <td>3.300833e-01</td>\n",
              "      <td>250.120109</td>\n",
              "      <td>0.041527</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.000000</td>\n",
              "      <td>-5.640751e+01</td>\n",
              "      <td>-7.271573e+01</td>\n",
              "      <td>-4.832559e+01</td>\n",
              "      <td>-5.683171e+00</td>\n",
              "      <td>-1.137433e+02</td>\n",
              "      <td>-2.616051e+01</td>\n",
              "      <td>-4.355724e+01</td>\n",
              "      <td>-7.321672e+01</td>\n",
              "      <td>-1.343407e+01</td>\n",
              "      <td>-2.458826e+01</td>\n",
              "      <td>-4.797473e+00</td>\n",
              "      <td>-1.868371e+01</td>\n",
              "      <td>-5.791881e+00</td>\n",
              "      <td>-1.921433e+01</td>\n",
              "      <td>-4.498945e+00</td>\n",
              "      <td>-1.412985e+01</td>\n",
              "      <td>-2.516280e+01</td>\n",
              "      <td>-9.498746e+00</td>\n",
              "      <td>-7.213527e+00</td>\n",
              "      <td>-5.449772e+01</td>\n",
              "      <td>-3.483038e+01</td>\n",
              "      <td>-1.093314e+01</td>\n",
              "      <td>-4.480774e+01</td>\n",
              "      <td>-2.836627e+00</td>\n",
              "      <td>-1.029540e+01</td>\n",
              "      <td>-2.604551e+00</td>\n",
              "      <td>-2.256568e+01</td>\n",
              "      <td>-1.543008e+01</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>54201.500000</td>\n",
              "      <td>-9.203734e-01</td>\n",
              "      <td>-5.985499e-01</td>\n",
              "      <td>-8.903648e-01</td>\n",
              "      <td>-8.486401e-01</td>\n",
              "      <td>-6.915971e-01</td>\n",
              "      <td>-7.682956e-01</td>\n",
              "      <td>-5.540759e-01</td>\n",
              "      <td>-2.086297e-01</td>\n",
              "      <td>-6.430976e-01</td>\n",
              "      <td>-5.354257e-01</td>\n",
              "      <td>-7.624942e-01</td>\n",
              "      <td>-4.055715e-01</td>\n",
              "      <td>-6.485393e-01</td>\n",
              "      <td>-4.255740e-01</td>\n",
              "      <td>-5.828843e-01</td>\n",
              "      <td>-4.680368e-01</td>\n",
              "      <td>-4.837483e-01</td>\n",
              "      <td>-4.988498e-01</td>\n",
              "      <td>-4.562989e-01</td>\n",
              "      <td>-2.117214e-01</td>\n",
              "      <td>-2.283949e-01</td>\n",
              "      <td>-5.423504e-01</td>\n",
              "      <td>-1.618463e-01</td>\n",
              "      <td>-3.545861e-01</td>\n",
              "      <td>-3.171451e-01</td>\n",
              "      <td>-3.269839e-01</td>\n",
              "      <td>-7.083953e-02</td>\n",
              "      <td>-5.295979e-02</td>\n",
              "      <td>5.600000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>84692.000000</td>\n",
              "      <td>1.810880e-02</td>\n",
              "      <td>6.548556e-02</td>\n",
              "      <td>1.798463e-01</td>\n",
              "      <td>-1.984653e-02</td>\n",
              "      <td>-5.433583e-02</td>\n",
              "      <td>-2.741871e-01</td>\n",
              "      <td>4.010308e-02</td>\n",
              "      <td>2.235804e-02</td>\n",
              "      <td>-5.142873e-02</td>\n",
              "      <td>-9.291738e-02</td>\n",
              "      <td>-3.275735e-02</td>\n",
              "      <td>1.400326e-01</td>\n",
              "      <td>-1.356806e-02</td>\n",
              "      <td>5.060132e-02</td>\n",
              "      <td>4.807155e-02</td>\n",
              "      <td>6.641332e-02</td>\n",
              "      <td>-6.567575e-02</td>\n",
              "      <td>-3.636312e-03</td>\n",
              "      <td>3.734823e-03</td>\n",
              "      <td>-6.248109e-02</td>\n",
              "      <td>-2.945017e-02</td>\n",
              "      <td>6.781943e-03</td>\n",
              "      <td>-1.119293e-02</td>\n",
              "      <td>4.097606e-02</td>\n",
              "      <td>1.659350e-02</td>\n",
              "      <td>-5.213911e-02</td>\n",
              "      <td>1.342146e-03</td>\n",
              "      <td>1.124383e-02</td>\n",
              "      <td>22.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>139320.500000</td>\n",
              "      <td>1.315642e+00</td>\n",
              "      <td>8.037239e-01</td>\n",
              "      <td>1.027196e+00</td>\n",
              "      <td>7.433413e-01</td>\n",
              "      <td>6.119264e-01</td>\n",
              "      <td>3.985649e-01</td>\n",
              "      <td>5.704361e-01</td>\n",
              "      <td>3.273459e-01</td>\n",
              "      <td>5.971390e-01</td>\n",
              "      <td>4.539234e-01</td>\n",
              "      <td>7.395934e-01</td>\n",
              "      <td>6.182380e-01</td>\n",
              "      <td>6.625050e-01</td>\n",
              "      <td>4.931498e-01</td>\n",
              "      <td>6.488208e-01</td>\n",
              "      <td>5.232963e-01</td>\n",
              "      <td>3.996750e-01</td>\n",
              "      <td>5.008067e-01</td>\n",
              "      <td>4.589494e-01</td>\n",
              "      <td>1.330408e-01</td>\n",
              "      <td>1.863772e-01</td>\n",
              "      <td>5.285536e-01</td>\n",
              "      <td>1.476421e-01</td>\n",
              "      <td>4.395266e-01</td>\n",
              "      <td>3.507156e-01</td>\n",
              "      <td>2.409522e-01</td>\n",
              "      <td>9.104512e-02</td>\n",
              "      <td>7.827995e-02</td>\n",
              "      <td>77.165000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>172792.000000</td>\n",
              "      <td>2.454930e+00</td>\n",
              "      <td>2.205773e+01</td>\n",
              "      <td>9.382558e+00</td>\n",
              "      <td>1.687534e+01</td>\n",
              "      <td>3.480167e+01</td>\n",
              "      <td>7.330163e+01</td>\n",
              "      <td>1.205895e+02</td>\n",
              "      <td>2.000721e+01</td>\n",
              "      <td>1.559499e+01</td>\n",
              "      <td>2.374514e+01</td>\n",
              "      <td>1.201891e+01</td>\n",
              "      <td>7.848392e+00</td>\n",
              "      <td>7.126883e+00</td>\n",
              "      <td>1.052677e+01</td>\n",
              "      <td>8.877742e+00</td>\n",
              "      <td>1.731511e+01</td>\n",
              "      <td>9.253526e+00</td>\n",
              "      <td>5.041069e+00</td>\n",
              "      <td>5.591971e+00</td>\n",
              "      <td>3.942090e+01</td>\n",
              "      <td>2.720284e+01</td>\n",
              "      <td>1.050309e+01</td>\n",
              "      <td>2.252841e+01</td>\n",
              "      <td>4.584549e+00</td>\n",
              "      <td>7.519589e+00</td>\n",
              "      <td>3.517346e+00</td>\n",
              "      <td>3.161220e+01</td>\n",
              "      <td>3.384781e+01</td>\n",
              "      <td>25691.160000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                Time            V1  ...         Amount          Class\n",
              "count  284807.000000  2.848070e+05  ...  284807.000000  284807.000000\n",
              "mean    94813.859575  3.919560e-15  ...      88.349619       0.001727\n",
              "std     47488.145955  1.958696e+00  ...     250.120109       0.041527\n",
              "min         0.000000 -5.640751e+01  ...       0.000000       0.000000\n",
              "25%     54201.500000 -9.203734e-01  ...       5.600000       0.000000\n",
              "50%     84692.000000  1.810880e-02  ...      22.000000       0.000000\n",
              "75%    139320.500000  1.315642e+00  ...      77.165000       0.000000\n",
              "max    172792.000000  2.454930e+00  ...   25691.160000       1.000000\n",
              "\n",
              "[8 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 188
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hKVDdlam4J5j",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b83e8593-d860-4811-9ba6-7f8c59e215a7"
      },
      "source": [
        "# There are no null values in the data\n",
        "data.isna().sum().max()"
      ],
      "execution_count": 189,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 189
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "inHHNdmX4KDW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 378
        },
        "outputId": "db9261d7-acff-46f1-ade0-3164a351d65a"
      },
      "source": [
        "print(\"The dataset contains\", len(data),\"transactions.\")\n",
        "print(\"Fraud transactions: %i (%.2f%%).\" % (data['Class'].value_counts()[1], data['Class'].value_counts()[1]/len(data) * 100))\n",
        "print(\"Legitimate transactions: %i (%.2f%%).\" % (data['Class'].value_counts()[0],data['Class'].value_counts()[0]/len(data) * 100))\n",
        "\n",
        "# Ploting the transactions by Class\n",
        "count_classes = data.value_counts(data['Class']).sort_index()\n",
        "count_classes.plot(kind = 'bar', title = \"Distribution by Class \\n Legitimate = 0; Fraud = 1\", xlabel = \"Class\", ylabel = \"Frequency\", rot = 0)"
      ],
      "execution_count": 190,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The dataset contains 284807 transactions.\n",
            "Fraud transactions: 492 (0.17%).\n",
            "Legitimate transactions: 284315 (99.83%).\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7efd4bc70898>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 190
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qs2rxTuimreh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 483
        },
        "outputId": "7458a81d-e6cc-4c39-b2bf-d1b3b5ae460b"
      },
      "source": [
        "# Plotting column 'Amount' against 'Class'\n",
        "# The graph shows that the majority of frauds happen in transactions with lower amounts\n",
        "\n",
        "data.plot(kind = 'scatter', x = 'Class', y = 'Amount')\n",
        "\n",
        "fraud_amount = data.loc[data['Class'] == 1, 'Amount']\n",
        "legit_amount = data.loc[data['Class'] == 0, 'Amount']\n",
        "\n",
        "print(\"\"\"\n",
        "Amounts of fraudulent transactions: \\n Mean: %d \\n Median: %d \\n Max Amount: %d \\n \\n\n",
        "Amounts of legitimate transactions: \\n Mean: %d \\n Median: %d \\n Max Amount: %d\n",
        "\"\"\"\n",
        "% (fraud_amount.mean(), fraud_amount.median(), fraud_amount.max(), legit_amount.mean(), legit_amount.median(), legit_amount.max()))"
      ],
      "execution_count": 191,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Amounts of fraudulent transactions: \n",
            " Mean: 122 \n",
            " Median: 9 \n",
            " Max Amount: 2125 \n",
            " \n",
            "\n",
            "Amounts of legitimate transactions: \n",
            " Mean: 88 \n",
            " Median: 22 \n",
            " Max Amount: 25691\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VELRJhPH3W36"
      },
      "source": [
        "# 3) Scaling\n",
        "\n",
        "As mentioned previously, a PCA was performed in the original dataset and the V features (V1 to V28) are the obtained Principal Components of that transformation. The only features which have not been transformed with PCA are 'Time' and 'Amount'.\n",
        "\n",
        "In order to perform a PCA the features must be normalized first. Hence, we can assume that is what the authors of the dataset did regarding the V features. Therefore, columns 'Time' and 'Amount' must be scaled (normalized) as the other columns."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4YxYtbxWpfiW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 224
        },
        "outputId": "4186dbcb-12d6-4e9e-9de7-8b347e1e85b6"
      },
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "\n",
        "# Create scaled columns 'scaled_amount' and 'scaled_time'\n",
        "data['scaled_amount'] = StandardScaler().fit_transform(data['Amount'].values.reshape(-1, 1))\n",
        "data['scaled_time'] = StandardScaler().fit_transform(data['Time'].values.reshape(-1, 1))\n",
        "\n",
        "# Removing old 'Amount' and 'Time' columns\n",
        "data.drop(['Amount', 'Time'], axis = 1, inplace = True)\n",
        "\n",
        "# Scaling complete\n",
        "data.head()"
      ],
      "execution_count": 192,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>V1</th>\n",
              "      <th>V2</th>\n",
              "      <th>V3</th>\n",
              "      <th>V4</th>\n",
              "      <th>V5</th>\n",
              "      <th>V6</th>\n",
              "      <th>V7</th>\n",
              "      <th>V8</th>\n",
              "      <th>V9</th>\n",
              "      <th>V10</th>\n",
              "      <th>V11</th>\n",
              "      <th>V12</th>\n",
              "      <th>V13</th>\n",
              "      <th>V14</th>\n",
              "      <th>V15</th>\n",
              "      <th>V16</th>\n",
              "      <th>V17</th>\n",
              "      <th>V18</th>\n",
              "      <th>V19</th>\n",
              "      <th>V20</th>\n",
              "      <th>V21</th>\n",
              "      <th>V22</th>\n",
              "      <th>V23</th>\n",
              "      <th>V24</th>\n",
              "      <th>V25</th>\n",
              "      <th>V26</th>\n",
              "      <th>V27</th>\n",
              "      <th>V28</th>\n",
              "      <th>Class</th>\n",
              "      <th>scaled_amount</th>\n",
              "      <th>scaled_time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.359807</td>\n",
              "      <td>-0.072781</td>\n",
              "      <td>2.536347</td>\n",
              "      <td>1.378155</td>\n",
              "      <td>-0.338321</td>\n",
              "      <td>0.462388</td>\n",
              "      <td>0.239599</td>\n",
              "      <td>0.098698</td>\n",
              "      <td>0.363787</td>\n",
              "      <td>0.090794</td>\n",
              "      <td>-0.551600</td>\n",
              "      <td>-0.617801</td>\n",
              "      <td>-0.991390</td>\n",
              "      <td>-0.311169</td>\n",
              "      <td>1.468177</td>\n",
              "      <td>-0.470401</td>\n",
              "      <td>0.207971</td>\n",
              "      <td>0.025791</td>\n",
              "      <td>0.403993</td>\n",
              "      <td>0.251412</td>\n",
              "      <td>-0.018307</td>\n",
              "      <td>0.277838</td>\n",
              "      <td>-0.110474</td>\n",
              "      <td>0.066928</td>\n",
              "      <td>0.128539</td>\n",
              "      <td>-0.189115</td>\n",
              "      <td>0.133558</td>\n",
              "      <td>-0.021053</td>\n",
              "      <td>0</td>\n",
              "      <td>0.244964</td>\n",
              "      <td>-1.996583</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.191857</td>\n",
              "      <td>0.266151</td>\n",
              "      <td>0.166480</td>\n",
              "      <td>0.448154</td>\n",
              "      <td>0.060018</td>\n",
              "      <td>-0.082361</td>\n",
              "      <td>-0.078803</td>\n",
              "      <td>0.085102</td>\n",
              "      <td>-0.255425</td>\n",
              "      <td>-0.166974</td>\n",
              "      <td>1.612727</td>\n",
              "      <td>1.065235</td>\n",
              "      <td>0.489095</td>\n",
              "      <td>-0.143772</td>\n",
              "      <td>0.635558</td>\n",
              "      <td>0.463917</td>\n",
              "      <td>-0.114805</td>\n",
              "      <td>-0.183361</td>\n",
              "      <td>-0.145783</td>\n",
              "      <td>-0.069083</td>\n",
              "      <td>-0.225775</td>\n",
              "      <td>-0.638672</td>\n",
              "      <td>0.101288</td>\n",
              "      <td>-0.339846</td>\n",
              "      <td>0.167170</td>\n",
              "      <td>0.125895</td>\n",
              "      <td>-0.008983</td>\n",
              "      <td>0.014724</td>\n",
              "      <td>0</td>\n",
              "      <td>-0.342475</td>\n",
              "      <td>-1.996583</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.358354</td>\n",
              "      <td>-1.340163</td>\n",
              "      <td>1.773209</td>\n",
              "      <td>0.379780</td>\n",
              "      <td>-0.503198</td>\n",
              "      <td>1.800499</td>\n",
              "      <td>0.791461</td>\n",
              "      <td>0.247676</td>\n",
              "      <td>-1.514654</td>\n",
              "      <td>0.207643</td>\n",
              "      <td>0.624501</td>\n",
              "      <td>0.066084</td>\n",
              "      <td>0.717293</td>\n",
              "      <td>-0.165946</td>\n",
              "      <td>2.345865</td>\n",
              "      <td>-2.890083</td>\n",
              "      <td>1.109969</td>\n",
              "      <td>-0.121359</td>\n",
              "      <td>-2.261857</td>\n",
              "      <td>0.524980</td>\n",
              "      <td>0.247998</td>\n",
              "      <td>0.771679</td>\n",
              "      <td>0.909412</td>\n",
              "      <td>-0.689281</td>\n",
              "      <td>-0.327642</td>\n",
              "      <td>-0.139097</td>\n",
              "      <td>-0.055353</td>\n",
              "      <td>-0.059752</td>\n",
              "      <td>0</td>\n",
              "      <td>1.160686</td>\n",
              "      <td>-1.996562</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.966272</td>\n",
              "      <td>-0.185226</td>\n",
              "      <td>1.792993</td>\n",
              "      <td>-0.863291</td>\n",
              "      <td>-0.010309</td>\n",
              "      <td>1.247203</td>\n",
              "      <td>0.237609</td>\n",
              "      <td>0.377436</td>\n",
              "      <td>-1.387024</td>\n",
              "      <td>-0.054952</td>\n",
              "      <td>-0.226487</td>\n",
              "      <td>0.178228</td>\n",
              "      <td>0.507757</td>\n",
              "      <td>-0.287924</td>\n",
              "      <td>-0.631418</td>\n",
              "      <td>-1.059647</td>\n",
              "      <td>-0.684093</td>\n",
              "      <td>1.965775</td>\n",
              "      <td>-1.232622</td>\n",
              "      <td>-0.208038</td>\n",
              "      <td>-0.108300</td>\n",
              "      <td>0.005274</td>\n",
              "      <td>-0.190321</td>\n",
              "      <td>-1.175575</td>\n",
              "      <td>0.647376</td>\n",
              "      <td>-0.221929</td>\n",
              "      <td>0.062723</td>\n",
              "      <td>0.061458</td>\n",
              "      <td>0</td>\n",
              "      <td>0.140534</td>\n",
              "      <td>-1.996562</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.158233</td>\n",
              "      <td>0.877737</td>\n",
              "      <td>1.548718</td>\n",
              "      <td>0.403034</td>\n",
              "      <td>-0.407193</td>\n",
              "      <td>0.095921</td>\n",
              "      <td>0.592941</td>\n",
              "      <td>-0.270533</td>\n",
              "      <td>0.817739</td>\n",
              "      <td>0.753074</td>\n",
              "      <td>-0.822843</td>\n",
              "      <td>0.538196</td>\n",
              "      <td>1.345852</td>\n",
              "      <td>-1.119670</td>\n",
              "      <td>0.175121</td>\n",
              "      <td>-0.451449</td>\n",
              "      <td>-0.237033</td>\n",
              "      <td>-0.038195</td>\n",
              "      <td>0.803487</td>\n",
              "      <td>0.408542</td>\n",
              "      <td>-0.009431</td>\n",
              "      <td>0.798278</td>\n",
              "      <td>-0.137458</td>\n",
              "      <td>0.141267</td>\n",
              "      <td>-0.206010</td>\n",
              "      <td>0.502292</td>\n",
              "      <td>0.219422</td>\n",
              "      <td>0.215153</td>\n",
              "      <td>0</td>\n",
              "      <td>-0.073403</td>\n",
              "      <td>-1.996541</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         V1        V2        V3  ...  Class  scaled_amount  scaled_time\n",
              "0 -1.359807 -0.072781  2.536347  ...      0       0.244964    -1.996583\n",
              "1  1.191857  0.266151  0.166480  ...      0      -0.342475    -1.996583\n",
              "2 -1.358354 -1.340163  1.773209  ...      0       1.160686    -1.996562\n",
              "3 -0.966272 -0.185226  1.792993  ...      0       0.140534    -1.996562\n",
              "4 -1.158233  0.877737  1.548718  ...      0      -0.073403    -1.996541\n",
              "\n",
              "[5 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 192
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LNuUqMEl-bJl"
      },
      "source": [
        "# 4) Unbalanced data and subsampling\n",
        "\n",
        "The large amount of identified legitimate transactions versus frauds suggests that this is an **unbalanced dataset**.\n",
        "\n",
        "By testing a model on an unbalanced dataset the accuracy and overall usefulness of such model can be seriously compromised due to:\n",
        "* Overfitting: the model will be unable to effectively understand and identify patterns in the data due to the higher amount of legitimate transactions.\n",
        "* Faulty correlations: as we will see, features in the unbalanced dataset hardly show any correlation, which could impact the performance of the model.\n",
        "\n",
        "There are a few methods that can be used to deal with this problem:\n",
        "1. Collect more data;\n",
        "2. Change the performance metric;\n",
        "3. Resample the dataset.\n",
        "\n",
        "In this section we will focus on the last solution by applying a **random under-sample** technique.\n",
        "\n",
        "In short, under-sampling removes instances of the over-represented class (in this case, legitimate transactions), in order to archive a balance between classes. Our approach will be to generate a subsample with a 50/50 ratio (i.e., same amount) of fraud and legitimate transactions.\n",
        "\n",
        "*Note: This approach has a few shortcomings that will be discussed in the later sections of the notebook.*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YzE-r6txFrtY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 565
        },
        "outputId": "8a652e91-fbf0-4a0d-f7df-6350109b59df"
      },
      "source": [
        "# To showcase the problems with the correlations in the unbalanced dataset, let us display the correlation matrix for the whole dataset.\n",
        "\n",
        "# Create sample figsize in inches\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "# Unbalanced DataFrame Correlation\n",
        "corr = data.corr()\n",
        "sns.heatmap(corr, cmap='BuGn', ax=ax)\n",
        "ax.set_title(\"Unbalanced Dataset Correlation Matrix\", fontsize=14)\n",
        "plt.show()"
      ],
      "execution_count": 193,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MsQw6ZTjzxeW"
      },
      "source": [
        "## 4.1) Training subsample\n",
        "### Generating a balanced subsample\n",
        "\n",
        "In this section we will apply the random under-sample technique to generate a \"balanced\" subsample, in which the number of legitimate transactions is equal to the number of fraudulent transactions.\n",
        "\n",
        "Steps:\n",
        "1. Determine the number of occurrences of the under-represented class (number of frauds = 492);\n",
        "2. Bring the number of the over-represented class \"down\" to the same amount (randomly select 492 legitimate transactions);\n",
        "3. And thus generate a subsample of the dataframe with a 50/50 ratio with regards to the classes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oZqJ_A5nzwCN",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 224
        },
        "outputId": "c436e0fa-b754-4566-9ed2-092539776283"
      },
      "source": [
        "# Generate balanced subsample\n",
        "\n",
        "# Shuffle the data to randomize selection of legitimate cases\n",
        "new_df = data.sample(frac=1)\n",
        "\n",
        "# Number of fraudulent transactions:\n",
        "no_fraud = data['Class'].value_counts()[1]      # 492\n",
        "\n",
        "# Separate dataset by class\n",
        "fraud_df = new_df.loc[new_df['Class'] == 1]\n",
        "legit_df = new_df.loc[new_df['Class'] == 0][:no_fraud]\n",
        "\n",
        "# Concatenate the two dataframes\n",
        "new_df = pd.concat([fraud_df, legit_df])\n",
        "# And shuffle the new dataframe\n",
        "new_df = new_df.sample(frac=1, random_state=19)\n",
        "\n",
        "new_df.head()"
      ],
      "execution_count": 194,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>V1</th>\n",
              "      <th>V2</th>\n",
              "      <th>V3</th>\n",
              "      <th>V4</th>\n",
              "      <th>V5</th>\n",
              "      <th>V6</th>\n",
              "      <th>V7</th>\n",
              "      <th>V8</th>\n",
              "      <th>V9</th>\n",
              "      <th>V10</th>\n",
              "      <th>V11</th>\n",
              "      <th>V12</th>\n",
              "      <th>V13</th>\n",
              "      <th>V14</th>\n",
              "      <th>V15</th>\n",
              "      <th>V16</th>\n",
              "      <th>V17</th>\n",
              "      <th>V18</th>\n",
              "      <th>V19</th>\n",
              "      <th>V20</th>\n",
              "      <th>V21</th>\n",
              "      <th>V22</th>\n",
              "      <th>V23</th>\n",
              "      <th>V24</th>\n",
              "      <th>V25</th>\n",
              "      <th>V26</th>\n",
              "      <th>V27</th>\n",
              "      <th>V28</th>\n",
              "      <th>Class</th>\n",
              "      <th>scaled_amount</th>\n",
              "      <th>scaled_time</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>161747</th>\n",
              "      <td>-1.716749</td>\n",
              "      <td>0.744803</td>\n",
              "      <td>-0.862187</td>\n",
              "      <td>-2.984856</td>\n",
              "      <td>2.295172</td>\n",
              "      <td>-0.697655</td>\n",
              "      <td>2.415072</td>\n",
              "      <td>-1.105404</td>\n",
              "      <td>1.546137</td>\n",
              "      <td>1.357559</td>\n",
              "      <td>0.444295</td>\n",
              "      <td>0.262570</td>\n",
              "      <td>0.167378</td>\n",
              "      <td>-0.757984</td>\n",
              "      <td>0.328306</td>\n",
              "      <td>-1.703165</td>\n",
              "      <td>-0.378330</td>\n",
              "      <td>-2.411445</td>\n",
              "      <td>-2.125987</td>\n",
              "      <td>0.196357</td>\n",
              "      <td>-0.175962</td>\n",
              "      <td>1.335261</td>\n",
              "      <td>0.085648</td>\n",
              "      <td>-0.877190</td>\n",
              "      <td>-0.324443</td>\n",
              "      <td>0.462089</td>\n",
              "      <td>-0.511687</td>\n",
              "      <td>-0.807434</td>\n",
              "      <td>0</td>\n",
              "      <td>-0.329241</td>\n",
              "      <td>0.414170</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>184873</th>\n",
              "      <td>-3.164983</td>\n",
              "      <td>-3.517903</td>\n",
              "      <td>-1.279115</td>\n",
              "      <td>2.117235</td>\n",
              "      <td>1.145741</td>\n",
              "      <td>-0.935345</td>\n",
              "      <td>0.355602</td>\n",
              "      <td>0.446354</td>\n",
              "      <td>-0.150547</td>\n",
              "      <td>-0.364924</td>\n",
              "      <td>-1.515967</td>\n",
              "      <td>0.090218</td>\n",
              "      <td>0.307483</td>\n",
              "      <td>0.694520</td>\n",
              "      <td>0.372070</td>\n",
              "      <td>-0.365522</td>\n",
              "      <td>-0.075789</td>\n",
              "      <td>0.803038</td>\n",
              "      <td>0.082372</td>\n",
              "      <td>1.923438</td>\n",
              "      <td>1.158343</td>\n",
              "      <td>1.608053</td>\n",
              "      <td>1.049287</td>\n",
              "      <td>0.623452</td>\n",
              "      <td>-0.761159</td>\n",
              "      <td>-0.370585</td>\n",
              "      <td>0.366321</td>\n",
              "      <td>-0.153810</td>\n",
              "      <td>0</td>\n",
              "      <td>1.611270</td>\n",
              "      <td>0.665665</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>230476</th>\n",
              "      <td>-0.099724</td>\n",
              "      <td>2.795414</td>\n",
              "      <td>-6.423856</td>\n",
              "      <td>3.247513</td>\n",
              "      <td>-1.632290</td>\n",
              "      <td>-2.766665</td>\n",
              "      <td>-2.312223</td>\n",
              "      <td>0.961014</td>\n",
              "      <td>-1.896001</td>\n",
              "      <td>-4.919348</td>\n",
              "      <td>3.053654</td>\n",
              "      <td>-5.297811</td>\n",
              "      <td>-1.466030</td>\n",
              "      <td>-7.035880</td>\n",
              "      <td>1.997132</td>\n",
              "      <td>-3.836189</td>\n",
              "      <td>-2.515183</td>\n",
              "      <td>-0.864579</td>\n",
              "      <td>2.328927</td>\n",
              "      <td>0.340898</td>\n",
              "      <td>0.647714</td>\n",
              "      <td>0.126576</td>\n",
              "      <td>0.203953</td>\n",
              "      <td>0.008495</td>\n",
              "      <td>-0.174501</td>\n",
              "      <td>0.575295</td>\n",
              "      <td>0.152876</td>\n",
              "      <td>-0.098173</td>\n",
              "      <td>1</td>\n",
              "      <td>0.025869</td>\n",
              "      <td>1.085118</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>137896</th>\n",
              "      <td>1.189148</td>\n",
              "      <td>0.245258</td>\n",
              "      <td>0.394312</td>\n",
              "      <td>0.729470</td>\n",
              "      <td>-0.428640</td>\n",
              "      <td>-0.811898</td>\n",
              "      <td>-0.048341</td>\n",
              "      <td>-0.032105</td>\n",
              "      <td>0.150417</td>\n",
              "      <td>-0.299429</td>\n",
              "      <td>0.284102</td>\n",
              "      <td>-0.078110</td>\n",
              "      <td>-0.801720</td>\n",
              "      <td>-0.050369</td>\n",
              "      <td>1.426423</td>\n",
              "      <td>0.135774</td>\n",
              "      <td>0.445773</td>\n",
              "      <td>-0.737617</td>\n",
              "      <td>-0.673108</td>\n",
              "      <td>-0.183587</td>\n",
              "      <td>-0.249394</td>\n",
              "      <td>-0.733556</td>\n",
              "      <td>0.210351</td>\n",
              "      <td>0.334025</td>\n",
              "      <td>0.067583</td>\n",
              "      <td>0.107092</td>\n",
              "      <td>-0.012416</td>\n",
              "      <td>0.028704</td>\n",
              "      <td>0</td>\n",
              "      <td>-0.345313</td>\n",
              "      <td>-0.261831</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>44223</th>\n",
              "      <td>-19.139733</td>\n",
              "      <td>9.286847</td>\n",
              "      <td>-20.134992</td>\n",
              "      <td>7.818673</td>\n",
              "      <td>-15.652208</td>\n",
              "      <td>-1.668348</td>\n",
              "      <td>-21.340478</td>\n",
              "      <td>0.641900</td>\n",
              "      <td>-8.550110</td>\n",
              "      <td>-16.649628</td>\n",
              "      <td>4.818152</td>\n",
              "      <td>-9.445315</td>\n",
              "      <td>1.317056</td>\n",
              "      <td>-7.243461</td>\n",
              "      <td>0.830910</td>\n",
              "      <td>-9.533257</td>\n",
              "      <td>-18.750641</td>\n",
              "      <td>-8.092649</td>\n",
              "      <td>3.326758</td>\n",
              "      <td>0.427203</td>\n",
              "      <td>-2.182692</td>\n",
              "      <td>0.520543</td>\n",
              "      <td>-0.760556</td>\n",
              "      <td>0.662767</td>\n",
              "      <td>-0.948454</td>\n",
              "      <td>0.121796</td>\n",
              "      <td>-3.381843</td>\n",
              "      <td>-1.256524</td>\n",
              "      <td>1</td>\n",
              "      <td>0.206103</td>\n",
              "      <td>-1.115288</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "               V1        V2         V3  ...  Class  scaled_amount  scaled_time\n",
              "161747  -1.716749  0.744803  -0.862187  ...      0      -0.329241     0.414170\n",
              "184873  -3.164983 -3.517903  -1.279115  ...      0       1.611270     0.665665\n",
              "230476  -0.099724  2.795414  -6.423856  ...      1       0.025869     1.085118\n",
              "137896   1.189148  0.245258   0.394312  ...      0      -0.345313    -0.261831\n",
              "44223  -19.139733  9.286847 -20.134992  ...      1       0.206103    -1.115288\n",
              "\n",
              "[5 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 194
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "71yGZXl1_ebQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "outputId": "f1599c6e-9632-4854-d928-4e8a72466fb7"
      },
      "source": [
        "# The subsample is balanced with regards to the classes\n",
        "\n",
        "print(\"\"\"\n",
        "Number of transactions in the balanced subsample: %i\n",
        "Number of fraudulent transactions: %i (%i%%)\n",
        "Number of legitimate transactions: %i (%i%%)\n",
        "\"\"\" % (len(new_df), new_df['Class'].value_counts()[1],new_df['Class'].value_counts()[1]/len(new_df)*100, new_df['Class'].value_counts()[0], new_df['Class'].value_counts()[0]/len(new_df)*100))\n",
        "\n",
        "# Ploting the transactions by Class in subsample\n",
        "count_classes_new_df = new_df.value_counts(new_df['Class']).sort_index()\n",
        "count_classes_new_df.plot(kind = 'bar', title = \"Distribution by Class \\n Legitimate = 0; Fraud = 1\", xlabel = \"Class\", ylabel = \"Frequency\", rot = 0)"
      ],
      "execution_count": 195,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Number of transactions in the balanced subsample: 984\n",
            "Number of fraudulent transactions: 492 (50%)\n",
            "Number of legitimate transactions: 492 (50%)\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7efd4c21d898>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 195
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ChYPlgQTHWKJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 565
        },
        "outputId": "d217d962-64d3-407e-eb27-ff1bb98f4cef"
      },
      "source": [
        "# Also, the previously mentioned problems with the correlations are now greatly reduced.\n",
        "\n",
        "fig, ax1 = plt.subplots(figsize=(12,8))\n",
        "\n",
        "# Balanced dataframe correlation\n",
        "corr = new_df.corr()\n",
        "sns.heatmap(corr, cmap='BuGn', ax = ax1)\n",
        "ax1.set_title(\"Unbalanced Dataset Correlation Matrix\", fontsize=14)\n",
        "plt.show()"
      ],
      "execution_count": 196,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qOGv4-LwP27e"
      },
      "source": [
        "# 5) Logistic Regression Classifier\n",
        "\n",
        "This section will be comprised as follows:\n",
        "\n",
        "1. Feature selection using Recursive Feature Elimination and Cross-Validation (RFECV). The pruned features will be removed from the balanced subsample.\n",
        "2. Splitting the new balanced dataset into training and testing subsets.\n",
        "3. Determine the parameters that give the best predictive cross-validation score using GridSearchCV.\n",
        "4. Logistic Regression model evaluation (cross-validation score, classification report, confusion matrix).\n",
        "\n",
        "\n",
        "The classifier will be evaluated regarding its accuracy measures.\n",
        "\n",
        "Finally, we'll generate predictions on the training data using the developed model."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EM_2goDkHy7k"
      },
      "source": [
        "### 1) Feature selection using RFECV\n",
        "\n",
        "RFECV performs Recursive Feature Elimination (RFE) in a cross-validation loop to find the optimal number or the best number of features. It also returns the best features to include in the model.\n",
        "\n",
        "[Source](https://scikit-learn.org/stable/modules/generated/sklearn.feature_selection.RFECV.html#sklearn.feature_selection.RFECV)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PqaA7XHr9hbr",
        "outputId": "f08b17cf-9c48-453f-b23b-ef004005435e"
      },
      "source": [
        "# Create X (features) and y (response/check)\n",
        "X = new_df.drop('Class',axis=1)\n",
        "y = new_df['Class']\n",
        "\n",
        "# Logistic Regression Model\n",
        "lr = LogisticRegression()\n",
        "\n",
        "# Use accuracy score as the scorer\n",
        "rfecv = RFECV(estimator = lr, step=1, cv=5, scoring='accuracy')\n",
        "rfecv.fit(X, y)\n",
        "\n",
        "print(\"Optimal number of features: %d\" % rfecv.n_features_)\n",
        "print('Selected features: %s' % list(X.columns[rfecv.support_]))\n",
        "\n",
        "# Removing pruned features from balanced subsample.\n",
        "X = X[list(X.columns[rfecv.support_])]"
      ],
      "execution_count": 197,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Optimal number of features: 13\n",
            "Selected features: ['V4', 'V6', 'V8', 'V10', 'V11', 'V12', 'V13', 'V14', 'V20', 'V22', 'V27', 'V28', 'scaled_amount']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-wwDp3ybIUL8"
      },
      "source": [
        "### 2) Split subsample into training and testing subsets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZZO9pEqbSNAE"
      },
      "source": [
        "# 80/20 split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=19)"
      ],
      "execution_count": 198,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_0rW3jtNMZaF"
      },
      "source": [
        "### 3) Determine the best parameters (GridSearchCV)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RhwRvez0Uzcs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "89beeccf-03d4-43e4-c6d6-ace862a9e127"
      },
      "source": [
        "# Fit a Logistic Regression classifier into the training data\n",
        "lr = LogisticRegression().fit(X_train, y_train)\n",
        "\n",
        "# We can check the cross-validation score of this \"untouched\" model:\n",
        "print(\"Pre-GridSearchCV Cross Validation Score: \", round(cross_val_score(lr, X_train, y_train).mean(),3)*100, \"%\")\n",
        "\n",
        "\n",
        "# Using GridSearchCV to figure out the parameters that return the best cross-validation score\n",
        "\n",
        "# Parameter grid:\n",
        "lr_params = {'penalty': ['l1', 'l2'], 'C': [0.001, 0.01, 0.1, 1, 10, 100, 1000]}\n",
        "\n",
        "grid_lr = GridSearchCV(estimator = LogisticRegression(), param_grid = lr_params)\n",
        "grid_lr.fit(X_train, y_train)\n",
        "\n",
        "# The Logistic Regression model with the best parameters:\n",
        "lr = grid_lr.best_estimator_\n",
        "print(\"\\nPost-GridSearchCV Cross Validation Score: \", round(cross_val_score(lr, X_train, y_train).mean(),3)*100, \"%\")"
      ],
      "execution_count": 199,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Pre-GridSearchCV Cross Validation Score:  95.0 %\n",
            "\n",
            "Post-GridSearchCV Cross Validation Score:  95.7 %\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2h8tDvDqQwSa"
      },
      "source": [
        "### 4) Logistic Regression model evaluation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Z8iMEG_fT_RX",
        "outputId": "a5ddd689-c5c9-487d-8787-8e50fa2c1408"
      },
      "source": [
        "# Evaluation on training set\n",
        "y_pred_train = lr.predict(X_train)\n",
        "y_pred_train_prob = lr.predict_log_proba(X_train)[:, 1]\n",
        "[fpr, tpr, thr] = roc_curve(y_train, y_pred_train_prob)\n",
        "training_score = accuracy_score(y_train, y_pred_train)\n",
        "\n",
        "print(lr.__class__.__name__, \" training accuracy score: %2.3f\" % training_score)\n",
        "print(lr.__class__.__name__,\" auc is %2.3f\" % auc(fpr, tpr))\n",
        "print(lr.__class__.__name__, \" training classification report:\", \"\\n\", classification_report(y_train, y_pred_train))"
      ],
      "execution_count": 200,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LogisticRegression  training accuracy score: 0.958\n",
            "LogisticRegression  auc is 0.987\n",
            "LogisticRegression  training classification report: \n",
            "               precision    recall  f1-score   support\n",
            "\n",
            "           0       0.93      0.99      0.96       393\n",
            "           1       0.99      0.92      0.96       394\n",
            "\n",
            "    accuracy                           0.96       787\n",
            "   macro avg       0.96      0.96      0.96       787\n",
            "weighted avg       0.96      0.96      0.96       787\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "id": "sy3iHFG7Tr9I",
        "outputId": "da33260b-fb12-4be2-994f-e3facb023a29"
      },
      "source": [
        "# Confusion Matrix on training set\n",
        "lr_cf_training = confusion_matrix(y_train, y_pred_train)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "sns.heatmap(lr_cf_training, ax=ax, annot=True, annot_kws={\"fontsize\":14}, cmap='BuGn')\n",
        "ax.set_title(\"Confusion Matrix \\n Logistic Regression | Training set\", fontsize=14)\n",
        "ax.set_xticklabels(['True: 0', 'True: 1'], fontsize=14)\n",
        "ax.set_yticklabels(['Predicted: 0', 'Predicted: 1'], fontsize=14, rotation=360)\n",
        "plt.show()"
      ],
      "execution_count": 201,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3+BfwFlmQsF1KaTRASulT4PdkX2m/TTaTwtl5n99Qt2/JAuG3yepFFwF+W7L9r2S1zMPzccwkpfQw2SwW2+f7PJsf05wyB8hmT5gXOCalNIos+z4d+A/wLlkA/G2+QFaGcBPZ+/Fy3nYP9V9r9Xgb63saWW1yX7KbF+8hq3E+Lu9iInACWT32ALJ66e1TSpPrOeWB+b735z8XIvu9zY65uGe344CxwP+Rzd7xcv76R5V/M/Bbsm8O3iSbsaNHvrm+3+9kYFXgTrIPBP3I/lu6MO9zILAF2U29z5L9zfckL+fJ9SLLSr9HVrPdWG24pDlQZPfMSNKsiYhjyGapWDz9BP5hiYg3gedTSn9q6bEULbInE7bNS3IqXkTsTPahZpm8tl6S6uTNhpLKEhFHkc3cMY5sbuUzyKZIq7ggOr9Jcluy7GIrsvmu18l/ai4XEd2Aj8m+DVmLrPTnAYNoSY0xkJZUrlXIakl/RlazezVZRroSTQf+SPa1fxXZ1/Hbp5Reb/AozS2WJStNakN2Y+lDZOVNktQgSzskSQ2K7FHZi6eU7m3psUjSnMRAWpIkSSqDpR1ziNhmBT/RSGqSKf/5b0sPQdJcYoF5qqKlx1BUjJMeH9Hi1+b0d5IkSVIZzEhLkiSpONHiiePCmJGWJEmSymBGWpIkScWp4LRtBV+aJEmSVBwz0pIkSSpOBddIG0hLkiSpOJUbR1vaIUmSJJXDjLQkSZKKU8GlHWakJUmSpDKYkZYkSVJxKjhtayAtSZKk4ljaIUmSJKmUGWlJkiQVp3IT0makJUmSpHKYkZYkSVJxqio3JW0gLUmSpOJUbhxtaYckSZJUDjPSkiRJKo7T30mSJEkqZUZakiRJxanchLQZaUmSJKkcZqQlSZJUHKe/kyRJkspQuXG0pR2SJElSOcxIS5IkqThOfydJkiSplBlpSZIkFcebDSVJkqQyVG4cbWmHJEmSVA4z0pIkSSqONxtKkiRJKmVGWpIkScWp3IS0gbQkSZIKVMGzdljaIUmSJJXBjLQkSZKKU7kJaTPSkiRJUjnMSEuSJKk4FTz9nYG0JEmSilPB9Q8VfGmSJElSccxIS5IkqTgVXNphRlqSJEkVJyIWiIhXI+LtiHg3Is7O2/tGxCcR8Va+dMzbIyIuj4ihETEwItZr7BxmpCVJklSclktIfwtslVKaFBGtgOcj4pF82wkppbtq7b890D5fNgKuyn/Wy4y0JEmSKk7KTMpXW+VLauCQnYEb8+NeBhaPiDYNncNAWpIkScWJKGZp0qljnoh4CxgLPJ5SeiXfdF5evnFJRMyfty0PDC85fETeVi8DaUmSJBWnqpglIrpHxOslS/fap04pTUspdQRWADpHxFrAKUAHYENgSeCkci/NGmlJkiTNdVJKfYA+Tdx3QkQ8DWyXUuqVN38bEf8Cjs/XRwIrlhy2Qt5WLzPSkiRJKk4LlXZExNIRsXj+ekFgG+D96rrniAhgF2BQfsj9wB/z2Ts2Br5MKY1u6BxmpCVJklSJ2gD9ImIesuTxHSmlByPiqYhYmmw+kbeAw/P9HwZ2AIYCk4EDGzuBgbQkSZKK00LT36WUBgKd6mjfqp79E3BUc85hIC1JkqTiVPlkQ0mSJEklzEhLkiSpOE2c83luZEZakiRJKoMZaUmSJBWnchPSBtKSJEkqTljaIUmSJKmUGWlJkiQVxoy0JEmSpBrMSEuSJKkwFZyQNiMtSZIklcOMtCRJkgpTVcEpaQNpSZIkFcabDSVJkiTVYEZakiRJhTEjLUmSJKkGM9KSJEkqTCVnpA2kJUmSVJgKjqMt7ZAkSZLKYUZakiRJhank0g4z0pIkSVIZzEhLkiSpMJWckTaQliRJUmGCyg2kLe2QJEmSymBGWpIkSYWp5NIOM9KSJElSGcxIS5IkqTAVnJA2Iy1JkiSVw4y0JEmSClNVwSlpA2lJkiQVxpsNJUmSJNVgRlqSJEmFMSMtSZIkqQYz0pIkSSpMBSekDaQlSZJUHEs7JEmSJNVgRlqSJEmFMSMtSZIkqQYz0pIkSSpMJWekDaQlSZJUmEoOpC3tkCRJkspgRlqSJEmFqeCEtBlpSZIkqRxmpCVJklQYa6QlSZIk1WBGWpIkSYWp5Iy0gbQkSZIKU1XBgbSlHZIkSao4EbFARLwaEW9HxLsRcXbevlJEvBIRQyPi9oiYL2+fP18fmm9v29g5DKQlSZJUmIhilib4FtgqpbQu0BHYLiI2Bi4ELkkprQL8Dzg43/9g4H95+yX5fg0ykJYkSVLFSZlJ+WqrfEnAVsBdeXs/YJf89c75Ovn2rtFIgbeBtCRJkgoTEYUsTTz3PBHxFjAWeBz4CJiQUvo+32UEsHz+enlgOEC+/UvgZw31byAtSZKkwkRR/4voHhGvlyzda587pTQtpdQRWAHoDHSYnddmIC010ZG/68bb1zzOl/cO5st7B/PiZfexQ+etGjxmjy124s2rH+XrBz5k2M0vc/wehxc+zsUXXowbT7qMCfe+x4R73+PGky5jsdaLztj+63U24d6zr2fUbW/w9QMf8vY1j3PgtnsVPi5Js9/1ffqw7557sOmGG9Bls03505FH8OGHQ1p6WNKPIqXUJ6W0QcnSp4F9JwBPA5sAi0dE9cx1KwAj89cjgRUB8u2LAZ83NIY5KpCOiN0jIpWsHxARkxo6psCxPBgRfVvi3JozjRg3mpOuO5/1jtyeDY7agafeeoF7z76etVdavc79t9twS/qf2ps+D93CWod25cjLT+Uvvz+Eo3Y+YJbG8XSvO+n2mz3q3d7/lN6st8pabHfKfmx3yn6st8pa3HTSZTO2b7rm+rzzyfvs/rfDWOvQrlz1wI30+cuF7LPlLvX2KWnO9Nprr7Ln3vvQr39/rv1XX+aZZx4OO+hgvpwwoaWHJs3QUqUdEbF0RCyev14Q2AYYTBZQ757v1g24L399f75Ovv2plFKiAdHIdvJgsrrT78lqR+4Gzkopfd3oVTRDROwO3JlSinx9QWCRlNLYJh4/DOidUuo1G8byIDA+pXRAM4/7PfA3oB1ZHc5pKaV7Gj1umxUa/kVojvT5vwdxyg096fPQLTNtu+WU3iw43wLsdvYhM9qO3vlATtzzCH7xh84z2nbaeGt67H8ca7ZdldGfj6X/0/dy9k2XMPX7qXWe8+led9L3sTvo99idM23r8ItVGHz9M2x27C68+O7rAGy25oY8f+k9rHbgFgwZ8XGdfd5++lXMUzUPu58z07dimgNN+c9/W3oImkNN/vprNtuoM5dc0ZsuW27Z0sPRHGCBeapafBLnlS7cupAY55OTnmjw2iJiHbKbB+chSx7fkVI6JyJWBm4DlgTeBPZLKX0bEQsANwGdgC+AvVNKdf8fZ66pD2R5Atif7G7HzYHrgNbAEXUMel5gWmMRfFOklKYAU2a1nx9LRGwC3A6cRfZhYzfgzojYLKX0SosOTrNVVVUVe2yxEwsvuBAvvvtGnfvM32o+vpn6TY22Kd99w4rL/JxfLrsCn342gt9s8GtuOfkKjrnqLJ4b+Aq/WGZ5rj6mJ/O3mo8T+pzb7HFtsvr6TJw8aUYQDfDCu68xacrXbLrmBvUG0osutAgjxo9u9vkkzVm+nvw106dPZ9FFF218Z+lH0lJPNkwpDSQLimu3f0xWL127/Rug/q9869DU0o5vU0pjUkrDU0r9gVvIpwqJiB4RMSgvw/iIbM6+1hGxWET0iYixETExIp6NiA1KO42IP0bEpxExOc8AL1tr+0ylHRGxQz5J9pSI+DwiHsgn3H4G+CVwUUSkWiUim+bnnxwRIyPiqohYtGT7QhHRNyImRcRnEXFqk9/Bmo4Fnk4pnZdSGpxSOg94Jm9XBVirbQcm3v8B3z78MVcf05NdexzCoGHv17nvo68/y86bbMs2629BRNB++ZX46+5ZxrfNkssAcNo+f+KiO6+m76N38PHoT3nm7Rc56brzOXyn/csa33JLLs24L2cu5xo7YTzLLbF0ncfsuFFXunbarM6suqS5y9/P78lqHVZn3Y4dW3oo0gwtOI904cp9RPgUsux0tZWAfcmi+O/IgumnyaYN2YksPd4NeCoiVkspjY6IjYC+wBnAncCWwPkNnTQitiOrX7kAODAf/2/IPhDsBrwN3ABcVXLM2sBjZFniQ8jS+Jfm+1XXx/Qiq5v5PVmh+VnAFmRZ5ep+epCVszT0q9sEuKJW26PA0Q1dl+YeH4z4iI6Hb8tirRdh9813pN+Jl9Ll+D14d9gHM+177cO30O7nv+S+s2+g1bzz8tXXk7jsnus5u9tfmZ5/YbN++3Xo3KEjJ+115IzjqqKKhRZYkOWWXIYxX4zlqmN6sl/X3WZsX3C+Bdh49U70PvqHjPUaB2/J8HGjmn09m665Af1P6c2f/3kmr33wVrOPlzTnuOjCC3hzwBv0vfkW5plnnpYejvST0OxAOiI6kwXNT5Y0zwfsn1L6LN9nK7InyCydl2cAnBERvyUrEfk7cAzwZJ61BRgSERvyw9Nl6nIGcFdK6fSStoH5z8kRMQ2YmFIaU7L9BOD2lNLFJddwBPBmRCwDTM7PeVBK6dF8+4Fk8wqWGg/MHC3VtBzwWa22z/L2meTTtGQpyg6LwwqtG+leLW3q91P5aNQwAAZ8+A4brrYuf9ntUA75x/F17n/ydedz6g0XsNwSyzDuy8/p2ulXAHw8+lMgKxE5+6ZLuPO5h2Y6dtyELLN8Zr9e9Lrzmhntt5x8Bf9+/mHufv6RGW2jPs/+7MZ8MY6lF5t5ystlFl+KMf8bV6NtszU35OHzbuTMfr24+sGbmvoWSJoDXXRBT/7z8MNc17cfK6y4YksPR6qhpUo7fgxNDaS3y0ss5iXLRN8H/Klk+4jqIDq3PrAQMK7Wm7cA2U14AKsDD9Q6z0s0HEh3IstiN8f6wCoRUTq/V/Wg2pEF0vPl5wYgpTQpIt4p7SSl1Bvo3cxzNyifpqUPeLPh3Koqqpi/1XwN7jN9+nRGfZ59tttny5158d3XGf/lFwAMGPoOHVZcZUZwXpdxEz6fEVRDVmc9dsL4Oo95afAbLLLQwmyyxvq89F5Wu73JGuuz8IKta9RNb772Rjx0bj/OuvFiLrvn+qZerqQ50IXnn8+jjzzCdX37stLKK7f0cKSflKYG0s+RZU6nAqNSSrWnE6g9e0cVWSZ28zr6+qpZI5x1VWQ3R15Sx7aRwKqz8VxjqFXnna+PqWNfzWV6HnwKD73yJMPHjWKRBRdm3612ocu6m7Dj6dmkNucfdDKdO3Rk6xP3BuBniy7BHlvsxDMDX2L+VvNx4LZ7sccWO/Hrv+4+o89zbr6UB//Wl0/HjuSOZx/g+2nfs1bbDnRerSMnXXdeneNoyPv/Hcojrz7NNcdeSPdLTgTgmmMv5IGXHp9xo+Gv19mEh87tx5UP3Ej/p+5l2bx2etr0aTMCfElzh/P/dg4P3n8/l1zRm0UXXZTx47JvnhZaaCEWau23nJozRMxRsy3PVk0NpCenlIY2o98BZAHk9AamDRkMbFyrrfZ6bW8CXYFr69n+HdkUJ7XHsmZ9489vkJyan/vjvK01sBbZ9HXN8RJZrfVFJW3bAC82sx/NgZZbcmluPvlylltiab78eiIDPxnM9qftz2OvPwtAm58tQ7s2v6xxzB+32Z2Lup9OELw0+A26HL9HjVrkx15/lh1P78YZfziG43c/jO+nfc+QkR/Tt46p7Zpq355Hc8VRf+PRntnNg/e/9DhH9/6hGuqAbfeg9YILccKeh3PCnj88IGbYmOGstP8mZZ9X0o/v9ltvBaD7QQfWaD/8yKM44mhvz5GK1tR5pJdKKe1Uz/YewO4ppbVK2oIsi704cCLwPlmd8HbAEyml/4uIjckCzNOAu4AuQE/gZyXzSB9ANi/0wvn6DmTlID2B/mQlGr8BrkkpTY6Ix8iC6cPIZhoZn88h+DJwI3ANMJHs8ZC/TSkdlvd7FdlNkQcBo4Azge2Bu6vnkY6Io4GjU0r1PloyIjbNr/t04F5gV+Ac4FeNTX9naYekpnIeaUlNNSfMI73qP7YvJMYZctwjLX5theTa8zmkdwCeIssefwDcAaxGFqiSUnqZrB76CLIbBncDejTS78Nkwen2ZOvBr+QAAB4dSURBVNnpZ8lm+5ie73Im2aMdPwLG5ccMJJuBo22+/9tkgXhpTffxZLOM3JP/HEQWEJdaKh9/Q+N7EdgbOCC/pj8CezmHtCRJ+qmKqqpCljlBoxlp/TjMSEtqKjPSkppqTshIr3bpjoXEOB8c+1CLX1u580hLkiRJjarkmw0r98okSZKkApmRliRJUmF8IIskSZJUBks7JEmSJNVgRlqSJEmFqeTSDjPSkiRJUhnMSEuSJKkwlVwjbSAtSZKkwljaIUmSJKkGM9KSJEkqTCWXdlTulUmSJEkFMiMtSZKkwlgjLUmSJKkGM9KSJEkqTCXXSBtIS5IkqThVlnZIkiRJKmFGWpIkSYWp5NKOyr0ySZIkqUBmpCVJklSYSp7+zkBakiRJhbG0Q5IkSVINZqQlSZJUGDPSkiRJkmowIy1JkqTCeLOhJEmSVAZLOyRJkiTVYEZakiRJhank0g4z0pIkSVIZzEhLkiSpMNZIS5IkSarBjLQkSZIKU8k10gbSkiRJKkxUVW4BROVemSRJklQgM9KSJEkqTCWXdpiRliRJkspgRlqSJEmFqeTp7wykJUmSVBhLOyRJkqS5SESsGBFPR8R7EfFuRByTt/eIiJER8Va+7FByzCkRMTQiPoiIbRs7hxlpSZIkFaYFSzu+B/6aUhoQEYsAb0TE4/m2S1JKvUp3jog1gL2BNYGfA09ExKoppWn1ncCMtCRJkipOSml0SmlA/noiMBhYvoFDdgZuSyl9m1L6BBgKdG7oHAbSkiRJKkxEFLI0cwxtgU7AK3nT0RExMCJuiIgl8rblgeElh42g4cDbQFqSJEnFiagqaInuEfF6ydK97vPHwsC/gWNTSl8BVwHtgI7AaODicq/NGmlJkiTNdVJKfYA+De0TEa3IguhbUkp358d9VrL9WuDBfHUksGLJ4SvkbfUyIy1JkqTiRFUxS2Onzeo/rgcGp5T+UdLepmS3XYFB+ev7gb0jYv6IWAloD7za0DnMSEuSJKkSbQbsD7wTEW/lbacC+0RERyABw4DDAFJK70bEHcB7ZDN+HNXQjB1gIC1JkqQCtdQDWVJKzwN1nfzhBo45DzivqecwkJYkSVJhKvkR4ZV7ZZIkSVKBzEhLkiSpMFUtVNrxYzAjLUmSJJXBjLQkSZIKE3Xe71cZzEhLkiRJZTAjLUmSpMJU8qwdBtKSJEkqTEvNI/1jqNyPCJIkSVKBzEhLkiSpMFHBedvKvTJJkiSpQGakJUmSVJhKrpE2kJYkSVJhqip41o7KvTJJkiSpQGakJUmSVBifbChJkiSpBjPSkiRJKoxPNpQkSZLKUMmzdlTuRwRJkiSpQGakJUmSVBhvNpQkSZJUgxlpSZIkFaaSbzas3CuTJEmSCmRGWpIkSYWpquAaaQNpSZIkFcbSDkmSJEk1mJGWJElSYXwgiyRJkqQazEhLkiSpMFHBeVsDaUmSJBXG0g5JkiRJNZiRliRJUmGc/k6SJElSDWakJUmSVJjwyYaSJElS81V5s6EkSZKkUmakJUmSVJhKnke6cq9MkiRJKpAZaUmSJBXGB7JIkiRJqsGMtCRJkgpTyQ9kMZCWJElSYSp5HunK/YggSZIkFciMtCRJkgpTyaUdlXtlkiRJUoHMSEuSJKkwlfyIcANpSZIkFcYnG0qSJElzkYhYMSKejoj3IuLdiDgmb18yIh6PiA/zn0vk7RERl0fE0IgYGBHrNXYOA2lJkiQVJiIKWZrge+CvKaU1gI2BoyJiDeBk4MmUUnvgyXwdYHugfb50B65q7AQG0pIkSao4KaXRKaUB+euJwGBgeWBnoF++Wz9gl/z1zsCNKfMysHhEtGnoHAbSkiRJKkwU9b+I7hHxesnSvd4xRLQFOgGvAMumlEbnm8YAy+avlweGlxw2Im+rlzcbSpIkqTBFzSOdUuoD9Gn8/LEw8G/g2JTSV6VlISmlFBGp3DGYkZYkSVJFiohWZEH0LSmlu/Pmz6pLNvKfY/P2kcCKJYevkLfVy0BakiRJhWmpmw0j2+l6YHBK6R8lm+4HuuWvuwH3lbT/MZ+9Y2Pgy5ISkDpZ2jGHGP/gsJYegqS5xILdOrT0ECTNJdLNQ1p6CC1pM2B/4J2IeCtvOxW4ALgjIg4GPgX2zLc9DOwADAUmAwc2dgIDaUmSJBWmqoUKIFJKzwP1pa671rF/Ao5qzjks7ZAkSZLKYEZakiRJhWniw1PmSgbSkiRJKkxVBQfSlnZIkiRJZTAjLUmSpMJU1Xu/39zPjLQkSZJUBjPSkiRJKow3G0qSJEll8GZDSZIkSTWYkZYkSVJhooLztpV7ZZIkSVKBzEhLkiSpMJVcI20gLUmSpMJUciBtaYckSZJUBjPSkiRJKkwlzyNtRlqSJEkqgxlpSZIkFaYKM9KSJEmSSpiRliRJUmEquUbaQFqSJEmFqYrKLYCo3CuTJEmSCmRGWpIkSYXxZkNJkiRJNZiRliRJUmG82VCSJEkqQ1UFB9KWdkiSJEllMCMtSZKkwoQ3G0qSJEkqZUZakiRJhankGmkDaUmSJBWmkgNpSzskSZKkMpiRliRJUmGigvO2lXtlkiRJUoHMSEuSJKkw1khLkiRJqsGMtCRJkgoTFZyRNpCWJElSYSztkCRJklSDGWlJkiQVpgoz0pIkSZJKmJGWJElSYbzZUJIkSSpDVVRuAUTlXpkkSZJUIDPSkiRJKkx4s6EkSZKkUmakJUmSVJhKfiCLgbQkSZIKU8mBtKUdkiRJqjgRcUNEjI2IQSVtPSJiZES8lS87lGw7JSKGRsQHEbFtU85hRlqSJEmFacGbDfsCvYEba7VfklLqVdoQEWsAewNrAj8HnoiIVVNK0xo6gRlpSZIkVZyU0nPAF03cfWfgtpTStymlT4ChQOfGDjKQliRJUmGqIgpZIqJ7RLxesnRv4pCOjoiBeenHEnnb8sDwkn1G5G0NX1sz3wtJkiSpxaWU+qSUNihZ+jThsKuAdkBHYDRw8ayMwRppSZIkFSbmoEeEp5Q+q34dEdcCD+arI4EVS3ZdIW9r0JxzZZIkSao4VUQhSzkiok3J6q5A9Ywe9wN7R8T8EbES0B54tbH+zEhLkiSp4kTErUAXYKmIGAGcBXSJiI5AAoYBhwGklN6NiDuA94DvgaMam7EDDKQlSZJUoKoWmv0upbRPHc3XN7D/ecB5zTmHpR2SJElSGcxIS5IkqTBRwY8IN5CWJElSYcq9MXBuYGmHJEmSVAYz0pIkSSpMJZd2mJGWJEmSymBGWpIkSYWpquCMtIG0JEmSCuPNhpIkSZJqMCMtSZKkwnizoSRJkqQazEhLkiSpMNZIS5IkSarBjLQkSZIKU8k10gbSkiRJKkwlzyNtaYckSZJUBjPSkiRJKow3G0qSJEmqwYy0JEmSClPBJdIG0pIkSSqONxtKkiRJqsGMtCRJkgoT3mwoSZIkqZQZaUmSJBWmkmukDaQlSZJUGOeRliRJklSDGWlJkiQVJiq4tMOMtCRJklQGM9KSJEkqjDcbSpIkSWVwHmlJkiRJNZiRliRJUmEqubTDjLQkSZJUBjPSkiRJKowZaUmSJEk1mJGWJElSYSp51g4DaUmSJBWmqnLjaEs7JEmSpHKYkZYkSVJhKrm0w4y0JEmSVAYz0pIkSSpMJU9/ZyAtSZKkwlRyIG1phyRJklQGM9KSJEkqjDcbSpIkSarBjLQkSZIKY430jyQido+IVLJ+QERMaqGxPBgRfVvi3Prp+Pdt/dn/97uy9Sad2XqTzhy637688NyzM7Y/88TjHHv4oezw61+x6TprMuC1V1twtJKa6sit/8Db59/Pl9cO4MtrB/DiWbezQ8cujR53zLbdGPz3//DNvwYxqvfz9Nzr+ELHufhCi3Lj4Rcxoc8bTOjzBjcefhGLLbTIjO2/Xr0z9/7lSkb1fp6vr3+bt8+/nwO3+H2hY1LliYhCljlBo4F0RPSNiJQvUyPi44joFRGtf4Tx3Q6s3NSdI2JYRBT7r07D518zIu7K36MUET1aaiyaOyy97HIceexx9L39Tm649Q7W77wRJx/7Z4YO+QCAKVOmsPa6nfjT8Se28EglNceIL8Zw0m29WO/0XdjgjN146r2XuffYf7L2iqvVe8zFfziFI7fel5Nuu4jVT9yeHS46lOfef22WxvH0aTfRbfNd693e/6h/sF7bNdju7wez3d8PZr22a3DT4RfN2L5p+/V4Z/gQdr/sz6x18k5c9eSt9Dn4b+yzyU6zNC7pxxARN0TE2IgYVNK2ZEQ8HhEf5j+XyNsjIi6PiKERMTAi1mvKOZpa2vEEsD/QCtgcuA5oDRxRx6DnBaallFLtbc2VUpoCTJnVfn5ECwHDgLuBc1t2KJobbLHlVjXWD//zMdxzx20MevttVll1Nbb/7e8AmPC//7XE8CSV6f4BT9ZYP/3OSzii6z5s0r4j7wz/YKb9V22zEn/aZj/WOfV3vD/qoxntb306uMZ+O3Xakh67/Yk1l2/P6Alj6f/Sg5x9d2+mTpva7DF2+Hk7tl93CzY7e29eHvoWAIfdcCbPn3krq7ZZiSGjP6Hn/VfXOObqJ29lyzU24vcbbsutLz3Y7HPqp6mq5W427Av0Bm4saTsZeDKldEFEnJyvnwRsD7TPl42Aq/KfDWpqace3KaUxKaXhKaX+wC3ALgAR0SMiBuVlGB8B3wKtI2KxiOiTfxKYGBHPRsQGpZ1GxB8j4tOImBwRDwLL1to+U2lHROwQEa9ExJSI+DwiHoiIBSLiGeCXwEXVGfSSYzbNzz85IkZGxFURsWjJ9oXyzPukiPgsIk5t4vtSQ0rptZTS8fl7NLmcPvTTNW3aNB5/5GGmTJ7M2ut2bOnhSJpNqqKKvTbekYUXWIgXh7xZ5z47r9eVj8cNZ7t1NuejfzzJJ5c8Rd/DLmTpRZecsc9v1v4Vtxx5Mb0fv5k1T96Bg649ld07b8v5ex5X1rg2WaUjE6dM4sUPB8xoe2HIG0z65ms2bd+p3uMWXXBh/jf5q7LOKf2YUkrPAV/Uat4Z6Je/7kcez+btN6bMy8DiEdGmsXOUWyM9hSw7XW0lYF9gD2BdsmD6IWB5YCegE/Ac8FT1oCJiI7JPCn2AjsADwDkNnTQitgPuBx4H1ge2BJ7Nr2M3YETeR5t8ISLWBh7Lj1s3368jcENJ172AbYDfA13z8W5R69w9SoNzaXb5aMgQum60AV026MRF555Dz0svp92qq7b0sCTNorVWWJWJ173Jt30HcfWBZ7PrpUczaMSQOvddeZkV+eXPlmfvjXfkgGtOYv+rT6RDm5V54LhrZtSCnrbzEVz00HX0fe5uPh47nGcGv8JJt/Xi8K57lzW+5RZfmnETZ/62a+xXX7DcYkvXecyOHbvQdY1N6PPU7WWdUz9NVRGFLBHRPSJeL1m6N2E4y6aURuevx/BDEnd5YHjJfiPytgY1e9aOiOhMFjSXfm81H7B/SumzfJ+tyILVpfPyDIAzIuK3ZCUifweOIUutn5dvHxIRGwIHN3D6M4C7Ukqnl7QNzH9OjohpwMSU0piS7ScAt6eULi65hiOANyNiGbLM8cHAQSmlR/PtB5K9gaXGAzN/HzcL8l94d4CLe19Jt0MOnZ3day7xi5Xa0u/OfzNp0iSefvwxzj39VHpf35d27du39NAkzYIPRn9Cx9N2ZrEFF2H3ztvR77AL6XLefrw74sOZ9q2KKhaYb372v/oEPhwzDID9rz6BIb0eY8OV1+bVjwayfts16bzyOpy006E1jlto/gVZbvGlGTNhHFcdeDb7bfa7GdsXnG8BNm7Xkd7dzpzRtsZJOzD889E016bt16P/Uf/gzzedy2sfD2z8AKlgKaU+ZAnZco9Ps5okbWogvV1eYjEvWSb6PuBPJdtHVAfRufXJ6oXH1bqrcgGgXf56dbIsdKmXaDiQ7kSWxW6O9YFVImKvkrbqQbUjC6Tny88NQEppUkS8U9pJSqk3WZ3NbFP6B/D5t9+b7f6JatVqPlb4xS8B6LDGmgweNIjbb76RU8/+WwuPTNKsmDptKh999l8ABgx7lw1XXpu/bHcAh1x32kz7jp4wjqnfT50RRAN8OGYY30/7nl/87Oe8+tFAqqqqOPue3tz56iMzHT/uq+zb6zP/fRm9Hr5+RvstR1zMv197lLtff2xG26j/jQVgzIRxLL3IEjP1tcyiSzLmy3E12jZbdX0ePuFazrzrMq5+8tZmvAsSc9rjWD6LiDYppdF5lcTYvH0ksGLJfivkbQ1qaiD9HFnmdCowKqVU+66Gr2utVwGfkd2YWNuPXVhVRXZz5CV1bBsJ+B265ijTp0/nu+++a+lhSJrNqiKYv9V8dW57YcgbtJq3FSsvsyIfj82+XV55mRWZd555+XT8KCALxjv8fOUZwXldxn31xYygGmDK1G8Y+9XndR7z0tC3WGTBhdmkfSde+jCr3d6kfScWXqA1L374Qy335qttwEPH9+Gsu6/gskf7zdSP1Lg5KpS+H+gGXJD/vK+k/eiIuI3sJsMvS0pA6tXUQHpySmloMwY5gKzmZHpK6eN69hkMbFyrrfZ6bW+S1TBfW8/274B56hjLmvWNP79Bcmp+7o/zttbAWsBHdR0jzS5XXvoPNt381yy73HJM/vprHnvkId58/TV69b4KgK++nMCY0aOZNHEiACP++18WXmQRfrbUUvxsqbprGCW1vJ57Hc9Dbz3D8M9Hs8gCrdl309/SZfWN2LFXVsJ5/p5/pXO7ddi6ZzcAnnj3Rd74ZBA3HNqTY2/OKh4v3e80Xh76Fq9/kn1Bes49/+TBv17Dp+NHcscrj/D9tGmstUJ7Ordbh5Nuu6jugTTg/VEf8cjbz3HNQefQ/fozALjmoHN4YMBTDBn9CZDNI/3QX/tw5ZP96f/iAyy72FIATJs+jfF11FdLc5KIuBXoAiwVESOAs8gC6Dsi4mDgU2DPfPeHgR2AoWTVCgc25RxFPdnwCeAF4L6IOBF4H1gO2A54IqX0f8DlwIsRcQpwF9mF1j/ZZeY84IGIGAr0J/uI8xvgmpTSZLKp5zaPiJvJZhoZD1wIvBwRVwPXABOBDsBvU0qH5WUc1wMXRsQ4YBRwJrUC8og4Gjg6pdShvsFFxHzAGvnqAsByEdERmNTMDyL6ifhi/HjOPvUkvhg/ntYLL8Iqq67KxVdezcab/QqA/3vmac4744dbAi44+ywADjr8SA458qgWGbOkxi232FLcfMRFLLfY0nw5eSIDh3/A9hcdwmPvPA9Am8WXpt0yP3yLnFJip4sP4/L9T+e5029hynff8vigFzjulp5Uzyb72DvPs2Ov7pyx61Ecv8PBfD99GkNGf0Lf/7un7HHu+8/juKLbGTx6Unb//f0DnuTofj/c93/A5rvReoGFOGHHQzhhx0NmtA8bN4KV/rLVTP1JdWmph6eklPapZ1PXOvZNQLP/jzUam+45sqf7LZVSqnP29fyhI7unlNaq1b4I2VzKvweWISv1eAE4LaX0Ub7PgcDZwNLAM2QzfVyRUop8+wFA75TSwiX9/o7sE8VaZEHxi8CeKaVvImJjsmB5NWD+kn42yMeyKVmA/DFwT0rpzHx7a7L5Ancj+xRyBVlaf3xK6YCS6zyrus963ou2wCd1bHo2pdSlvuPAGmlJTbfUwWs0vpMkAenmIS1eV/HmF58VEuN0WnLZFr+2RgNp/TgMpCU1lYG0pKaaEwLptwoKpDvOAYF0UaUdkiRJEjFn3Ww4W5X7QBZJkiTpJ82MtCRJkgrTQvca/ijMSEuSJEllMCMtSZKkAlVuStpAWpIkSYXxZkNJkiRJNZiRliRJUmEqNx9tRlqSJEkqixlpSZIkFSYqeP47M9KSJElSGQykJUmSpDJY2iFJkqTCOP2dJEmSpBrMSEuSJKkw3mwoSZIkqQYz0pIkSSpM5eajDaQlSZJUIG82lCRJklSDgbQkSZJUBgNpSZIkqQzWSEuSJKkwlTz9nYG0JEmSCuPNhpIkSZJqMCMtSZKkwlRuPtqMtCRJklQWM9KSJEkqTgXfbGhGWpIkSSqDGWlJkiQVpnLz0QbSkiRJKpDT30mSJEmqwYy0JEmSCmNGWpIkSVINZqQlSZJUmAqe/c5AWpIkSUWq3Eja0g5JkiSpDGakJUmSVJjKzUebkZYkSZLKYkZakiRJhYkKvtvQQFqSJEmFcR5pSZIkSTWYkZYkSVJhKjcfbUZakiRJKosZaUmSJBWocnPSZqQlSZKkMpiRliRJUmFacva7iBgGTASmAd+nlDaIiCWB24G2wDBgz5TS/8rp34y0JEmSChMF/a8ZtkwpdUwpbZCvnww8mVJqDzyZr5fFQFqSJEk/JTsD/fLX/YBdyu3IQFqSJElznYjoHhGvlyzd69gtAY9FxBsl25dNKY3OX48Bli13DNZIS5Ikaa6TUuoD9Glkt1+llEZGxDLA4xHxfq0+UkSkcsdgRlqSJEmFiYKWpkgpjcx/jgXuAToDn0VEG4D859hyr81AWpIkSYWJKGZp/LzROiIWqX4N/AYYBNwPdMt36wbcV+61WdohSZKkSrQscE9kUfe8QP+U0n8i4jXgjog4GPgU2LPcExhIS5IkqeKklD4G1q2j/XOg6+w4h6UdkiRJUhnMSEuSJKkwzXx4ylzFjLQkSZJUBgNpSZIkqQyWdkiSJKkwTZmqbm5lRlqSJEkqg4G0JEmSVAYDaUmSJKkM1khLkiSpMBVcIm0gLUmSpOJUciBtaYckSZJUBgNpSZIkqQwG0pIkSVIZrJGWJElSYSr5gSwG0pIkSSpQ5UbSlnZIkiRJZTAjLUmSpMJUbj7ajLQkSZJUFgNpSZIkqQyWdkiSJKkwlnZIkiRJqsGMtCRJkgpTyfNIm5GWJEmSymAgLUmSJJXBQFqSJEkqgzXSkv6/vXsHkasK4wD+/4SgWESQYAxpIgbEiLiiCIqvxkZiES1EtNhCYhRMpZVYR0FREGI0IrERBCViEVBESCVCND4KFURtonlIiKJG8HEsdhbHUePuncxjJ78fDMwczr333GLP/Dnz3bMAMDIzXCJtRRoAALoQpAEAoAOlHQAAjEzN8P53VqQBAKADQRoAADpQ2gEAwMjMbmGHFWkAAOhEkAYAgA4EaQAA6ECNNAAAIzPLNdKCNAAAIzPD20gr7QAAgC4EaQAA6ECQBgCADtRIAwAwMjNcIm1FGgAAurAiDQDACM3umrQgDQDAyNj+DgAA+BtBGgAAOhCkAQCgAzXSAACMzAyXSKdaa5MeA/Afqmpra+35SY8DmH7mCxg/pR0w3bZOegDAimG+gDETpAEAoANBGgAAOhCkYbqpdwSWynwBY+ZhQwAA6MCKNAAAdCBIAwBAB4I0DKGq2v+89kzBGG+qqver6peq+rKqtk16THAmmvb5oqrWVdXLVfVZVf0+6fHASuA/G8Jw1vW935xk90Dbyf7OVbWqtfbrOAbWu95FSfYleTHJPUmuT7Kzqo611l4b1ziAJFM+XyQ5O8l3SR6LPalhSaxIwxBaa4cXX0lO9LclOSfJiaq6q6reqaqTSe6rqvmq+rH/PFV1c29Fak1f23VVtb+qfq6qQ1X1bFWtXuYQtyX5prX2YGvt09ba7iQvJXlomPsGlm/a54vW2tette2ttT1Jjg97v3AmEKRh9HYk2ZlkU5LXl3JAVV2e5K0kbyS5IsntSeaysLK82Ge+92W64RSnurZ3nn5vJrm6qlYtcfzA+ExyvgCWSWkHjN4zrbVXFz9U1VKOeTjJK621J/uOuz/Jwaq6oLV2NMn3ST5Pcqqffi9M8vZA25Es/O2vSfLtku4AGJdJzhfAMgnSMHoHOhxzVZKNVXVnX9viN+rFSY621vYm2Tvs4ICpYr6AFUSQhtH7aeDzH/nrS27RYJnFWUleSPLUv5zv0DKufTjJ2oG2tUl+y8JDRcB0meR8ASyTIA3jdyzJuVW1urX2Q69tbqDPB0kua619MeS13k2yZaDtliQHxrwbANDNOOcLYJk8bAjj914WVp12VNXGqrojyQMDfR5Pck1V7aqqK3v9NlfVc4sdqmpLb7/X9ae41q4k66vq6aq6tKruTTKf5InTe0vAiIxzvkhVzVXVXJLVSc7vfd50mu8JZoYgDWPWWjue5O4srAx/koX9Wh8d6PNxkhuTbEiyP8lHWXia/0hft/OSXJJ//szbf56vktzaO9eHSR5Jst0e0rAyjHO+6DnYe92Q5Lbe+31D3gbMrGqtTXoMAACw4liRBgCADgRpAADoQJAGAIAOBGkAAOhAkAYAgA4EaQAA6ECQBgCADgRpAADoQJAGAIAO/gQXtW6UfWaWVgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AtSDnQ1UVy8A",
        "outputId": "71859bfc-c4a4-4685-c626-f00637885faf"
      },
      "source": [
        "# Evaluation on test set (predictions)\n",
        "y_pred = lr.predict(X_test)\n",
        "y_pred_prob = lr.predict_log_proba(X_test)[:, 1]\n",
        "[fpr, tpr, thr] = roc_curve(y_test, y_pred_prob)\n",
        "testing_score = accuracy_score(y_test, y_pred)\n",
        "\n",
        "print(lr.__class__.__name__, \" training accuracy score: %2.3f\" % testing_score)\n",
        "print(lr.__class__.__name__,\" auc is %2.3f\" % auc(fpr, tpr))\n",
        "print(lr.__class__.__name__, \"testing classification report:\", \"\\n\", classification_report(y_test, y_pred))"
      ],
      "execution_count": 202,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "LogisticRegression  training accuracy score: 0.929\n",
            "LogisticRegression  auc is 0.987\n",
            "LogisticRegression testing classification report: \n",
            "               precision    recall  f1-score   support\n",
            "\n",
            "           0       0.90      0.97      0.93        99\n",
            "           1       0.97      0.89      0.93        98\n",
            "\n",
            "    accuracy                           0.93       197\n",
            "   macro avg       0.93      0.93      0.93       197\n",
            "weighted avg       0.93      0.93      0.93       197\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "q2Bu6OqbTWqI",
        "outputId": "ddae4666-bce7-42bf-ec75-7ef4e7fb4b5b"
      },
      "source": [
        "# ROC Curve\n",
        "\n",
        "idx = np.min(np.where(tpr > 0.95)) # index of the first threshold for which the sensibility > 0.95\n",
        "\n",
        "plt.figure()\n",
        "plt.plot(fpr, tpr, color='darkgreen', label='ROC curve (area = %0.3f)' % auc(fpr, tpr))\n",
        "plt.plot([0, 1], [0, 1], 'k--')\n",
        "plt.plot([0,fpr[idx]], [tpr[idx],tpr[idx]], 'k--', color='lightblue')\n",
        "plt.plot([fpr[idx],fpr[idx]], [0,tpr[idx]], 'k--', color='lightblue')\n",
        "plt.xlim([0.0, 1.0])\n",
        "plt.ylim([0.0, 1.05])\n",
        "plt.xlabel('False Positive Rate (1 - specificity)', fontsize=14)\n",
        "plt.ylabel('True Positive Rate (recall)', fontsize=14)\n",
        "plt.title('Receiver operating characteristic (ROC) curve')\n",
        "plt.legend(loc=\"lower right\")\n",
        "plt.show()\n",
        "\n",
        "print(\"\\nUsing a threshold of %.3f \" % thr[idx] + \"guarantees a sensitivity of %.3f \" % tpr[idx] +  \n",
        "      \"and a specificity of %.3f\" % (1-fpr[idx]) + \n",
        "      \", i.e. a false positive rate of %.2f%%.\" % (np.array(fpr[idx])*100))\n"
      ],
      "execution_count": 203,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Using a threshold of -1.593 guarantees a sensitivity of 0.969 and a specificity of 0.929, i.e. a false positive rate of 7.07%.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "id": "jvIzfA0sdi1p",
        "outputId": "0f79f1f7-7592-4c59-c204-9e15441bbaac"
      },
      "source": [
        "# Confusion Matrix on training set\n",
        "lr_cf= confusion_matrix(y_test, y_pred)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(12,8))\n",
        "\n",
        "sns.heatmap(lr_cf, ax=ax, annot=True, annot_kws={\"fontsize\":14}, cmap='BuGn')\n",
        "ax.set_title(\"Confusion Matrix \\n Logistic Regression | Test set\", fontsize=14)\n",
        "ax.set_xticklabels(['True: 0', 'True: 1'], fontsize=14)\n",
        "ax.set_yticklabels(['Predicted: 0', 'Predicted: 1'], fontsize=14, rotation=360)\n",
        "plt.show()"
      ],
      "execution_count": 204,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x576 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "scPO_VsPFmPQ"
      },
      "source": [
        "# 6) Conclusions\n",
        "\n",
        "* The model has an accuracy score of 0.93\n",
        "* A precision of 0.90\n",
        "* And a recall of 0.987\n",
        "* Area under the ROC Curve: 0.986\n",
        "\n",
        "*Note: Results might vary due to the random subsample generation (section 4.1).*"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NgwuS9UV4h_E"
      },
      "source": [
        "# 7) Improvements and Next Steps\n",
        "\n",
        "1. Problems with random under-sampling\n",
        "\n",
        "The main issue with random under-sampling is information loss, since we generate from a dataset with 284,807 observations a sample with (only) 984 transactions.\n",
        "\n",
        "**Possible solution**: Apply other subsampling technique, for example [SMOTE](https://machinelearningmastery.com/smote-oversampling-for-imbalanced-classification/).\n",
        "\n",
        "2. Under/over-sampling during cross-validation\n",
        "\n",
        "When dealing with unbalanced dataset, the order of events in the process of sampling take a whole other level of importance. It is highly recommended to **perform sampling during cross-validation** to avoid overfitting and \"data-leakage\" problems. Such technique would also allow to use the whole dataset for training and testing. [Learn more](https://www.marcoaltini.com/blog/dealing-with-imbalanced-data-undersampling-oversampling-and-proper-cross-validation).\n",
        "\n",
        "3. Lack of data pre-processing\n",
        "\n",
        "There is still room to perform more data pre-processing, for instance by inspecting the data for outliers or extremely correlated features.\n",
        "\n",
        "4. Testing other classifiers\n",
        "\n",
        "Despite the robustness of Logistic Regression, an interesting exercise would be to evaluate the performance of this classifier against other algorithms, such as Random Forest, Decision Tree, Support Vector Classifier, etc."
      ]
    }
  ]
}