Imbalanced Dataset_Overfitting_CreditCard_Fraud.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "3KzMVGQlLsve",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Kaggle's Credit Card Fraud Dataset -  (IMBALANCED DATASET)\n",
    "\n",
    "The data is from: https://www.kaggle.com/mlg-ulb/creditcardfraud\n",
    "\n",
    "It is important that credit card companies are able to recognize fraudulent credit card transactions so that customers are not charged for items that they did not purchase.\n",
    "\n",
    "<b>Context</b><br>\n",
    "The datasets contains transactions made by credit cards in September 2013 by european cardholders. This dataset presents transactions that occurred in two days, where we have 492 frauds out of 284,807 transactions. The dataset is highly unbalanced, the positive class (frauds) account for 0.172% of all transactions.\n",
    "\n",
    "Reference: Machine Learning Course (Professor S.R Das, Santa Clara University)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import pandas as pd\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# print all the outputs in a cell\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "#import os\n",
    "#from ipypublish import nb_setup\n",
    "#%load_ext rpy2.ipython\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score, roc_auc_score, confusion_matrix, classification_report\n",
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Read the data file\n",
    "cc = pd.read_csv(\"DSTMAA_data/creditcard.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Data Exploration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 28 anonymized variables (V1 to V28) in the data set. It contains only numerical input variables which are the result of a PCA transformation. Unfortunately, due to confidentiality issues, we did not have the original features and more background information about the data. Features V1, V2, ... V28 are the principal components obtained with PCA, the only features which have not been transformed with PCA are 'Time' and 'Amount'. Feature 'Time' contains the seconds elapsed between each transaction and the first transaction in the dataset. The feature 'Amount' is the transaction Amount, this feature can be used for example-dependant cost-senstive learning. Feature 'Class' is the response variable and it takes value 1 in case of fraud and 0 otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th {\n",
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       "\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>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>...</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>...</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>...</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",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Time        V1        V2        V3        V4        V5        V6        V7  \\\n",
       "0   0.0 -1.359807 -0.072781  2.536347  1.378155 -0.338321  0.462388  0.239599   \n",
       "1   0.0  1.191857  0.266151  0.166480  0.448154  0.060018 -0.082361 -0.078803   \n",
       "\n",
       "         V8        V9  ...         V21       V22       V23       V24  \\\n",
       "0  0.098698  0.363787  ...   -0.018307  0.277838 -0.110474  0.066928   \n",
       "1  0.085102 -0.255425  ...   -0.225775 -0.638672  0.101288 -0.339846   \n",
       "\n",
       "        V25       V26       V27       V28  Amount  Class  \n",
       "0  0.128539 -0.189115  0.133558 -0.021053  149.62      0  \n",
       "1  0.167170  0.125895 -0.008983  0.014724    2.69      0  \n",
       "\n",
       "[2 rows x 31 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Total number of observations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(284807, 31)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Total number of Fradulent Transactions (1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "492"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.Class.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Percentage of fradulent transactions in the data. <b>Data is highly imbalanced.<b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1727485630620034"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.Class.mean()*100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "'Time' contains the seconds elapsed between each transaction and the first transaction in the dataset. <br>In one day we have 24x60x60 = 86,400 seconds. Therefore, in two days we have 172800 seconds. <br><br> Assuming time starts at midnight of first day, then we can see that in the morning at 8:30 AM number of transactions picked up (i.e. after 8.33 hours or 30,000 seconds later). It is just showing the elapsed time. nothing much. We will drop this variable.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12e92aaa940>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e929a7f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(cc.Time, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amount is the only variable which is remaining. It is important variable as fradulent transaction normally don't follow the regular pattern. Also, this variable is not used in PCA transformation. Exploring amount variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    284807.000000\n",
       "mean         88.349619\n",
       "std         250.120109\n",
       "min           0.000000\n",
       "25%           5.600000\n",
       "50%          22.000000\n",
       "75%          77.165000\n",
       "max       25691.160000\n",
       "Name: Amount, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc.Amount.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above summary indicates the possibility of outliers as 75 percentile of the amount is around 77 dollars but maximum amount is 25,691 dollars (Huge gap). <br>Also, plotting histogram to see this visually. Below histogram indicates there are very few transactions at the higher amounts. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x12e92b7a2e8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e92b2ed30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(cc.Amount, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are only 7 transactions which are greater than 10,000 dollars and all of these transactions are non-fradulent (Class 0). Therefore, removing these outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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>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>...</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>46841</th>\n",
       "      <td>42951.0</td>\n",
       "      <td>-23.712839</td>\n",
       "      <td>-42.172688</td>\n",
       "      <td>-13.320825</td>\n",
       "      <td>9.925019</td>\n",
       "      <td>-13.945538</td>\n",
       "      <td>5.564891</td>\n",
       "      <td>15.710644</td>\n",
       "      <td>-2.844253</td>\n",
       "      <td>-1.580725</td>\n",
       "      <td>...</td>\n",
       "      <td>7.921600</td>\n",
       "      <td>-6.320710</td>\n",
       "      <td>-11.310338</td>\n",
       "      <td>0.404175</td>\n",
       "      <td>-4.547278</td>\n",
       "      <td>-1.577118</td>\n",
       "      <td>-2.357385</td>\n",
       "      <td>2.253662</td>\n",
       "      <td>12910.93</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54018</th>\n",
       "      <td>46253.0</td>\n",
       "      <td>-21.780665</td>\n",
       "      <td>-38.305310</td>\n",
       "      <td>-12.122469</td>\n",
       "      <td>9.752791</td>\n",
       "      <td>-12.880794</td>\n",
       "      <td>4.256017</td>\n",
       "      <td>14.785051</td>\n",
       "      <td>-2.818253</td>\n",
       "      <td>-0.667338</td>\n",
       "      <td>...</td>\n",
       "      <td>7.437478</td>\n",
       "      <td>-5.619439</td>\n",
       "      <td>-10.547038</td>\n",
       "      <td>0.653249</td>\n",
       "      <td>-4.232409</td>\n",
       "      <td>-0.480459</td>\n",
       "      <td>-2.257913</td>\n",
       "      <td>2.082488</td>\n",
       "      <td>11898.09</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>58465</th>\n",
       "      <td>48401.0</td>\n",
       "      <td>-36.802320</td>\n",
       "      <td>-63.344698</td>\n",
       "      <td>-20.645794</td>\n",
       "      <td>16.715537</td>\n",
       "      <td>-20.672064</td>\n",
       "      <td>7.694002</td>\n",
       "      <td>24.956587</td>\n",
       "      <td>-4.730111</td>\n",
       "      <td>-2.687312</td>\n",
       "      <td>...</td>\n",
       "      <td>11.455313</td>\n",
       "      <td>-10.933144</td>\n",
       "      <td>-17.173665</td>\n",
       "      <td>1.180700</td>\n",
       "      <td>-7.025783</td>\n",
       "      <td>-2.534330</td>\n",
       "      <td>-3.602479</td>\n",
       "      <td>3.450224</td>\n",
       "      <td>19656.53</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>151296</th>\n",
       "      <td>95286.0</td>\n",
       "      <td>-34.549296</td>\n",
       "      <td>-60.464618</td>\n",
       "      <td>-21.340854</td>\n",
       "      <td>16.875344</td>\n",
       "      <td>-19.229075</td>\n",
       "      <td>6.335259</td>\n",
       "      <td>24.422716</td>\n",
       "      <td>-4.964566</td>\n",
       "      <td>0.188912</td>\n",
       "      <td>...</td>\n",
       "      <td>11.502580</td>\n",
       "      <td>-9.499423</td>\n",
       "      <td>-16.513186</td>\n",
       "      <td>0.744341</td>\n",
       "      <td>-7.081325</td>\n",
       "      <td>-2.604551</td>\n",
       "      <td>-3.550963</td>\n",
       "      <td>3.250802</td>\n",
       "      <td>18910.00</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>169457</th>\n",
       "      <td>119713.0</td>\n",
       "      <td>-20.924897</td>\n",
       "      <td>-37.943452</td>\n",
       "      <td>-14.060281</td>\n",
       "      <td>10.473005</td>\n",
       "      <td>-10.866639</td>\n",
       "      <td>6.256654</td>\n",
       "      <td>14.960521</td>\n",
       "      <td>-2.392155</td>\n",
       "      <td>-0.597076</td>\n",
       "      <td>...</td>\n",
       "      <td>6.829810</td>\n",
       "      <td>-6.926353</td>\n",
       "      <td>-9.928657</td>\n",
       "      <td>-0.447084</td>\n",
       "      <td>-4.848151</td>\n",
       "      <td>-2.241620</td>\n",
       "      <td>-2.140723</td>\n",
       "      <td>2.001492</td>\n",
       "      <td>11789.84</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274771</th>\n",
       "      <td>166198.0</td>\n",
       "      <td>-35.548539</td>\n",
       "      <td>-31.850484</td>\n",
       "      <td>-48.325589</td>\n",
       "      <td>15.304184</td>\n",
       "      <td>-113.743307</td>\n",
       "      <td>73.301626</td>\n",
       "      <td>120.589494</td>\n",
       "      <td>-27.347360</td>\n",
       "      <td>-3.872425</td>\n",
       "      <td>...</td>\n",
       "      <td>-21.620120</td>\n",
       "      <td>5.712303</td>\n",
       "      <td>-1.581098</td>\n",
       "      <td>4.584549</td>\n",
       "      <td>4.554683</td>\n",
       "      <td>3.415636</td>\n",
       "      <td>31.612198</td>\n",
       "      <td>-15.430084</td>\n",
       "      <td>25691.16</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>284249</th>\n",
       "      <td>172273.0</td>\n",
       "      <td>-9.030538</td>\n",
       "      <td>-11.112584</td>\n",
       "      <td>-16.233798</td>\n",
       "      <td>3.592021</td>\n",
       "      <td>-40.427726</td>\n",
       "      <td>23.917837</td>\n",
       "      <td>44.054461</td>\n",
       "      <td>-7.277778</td>\n",
       "      <td>-4.210637</td>\n",
       "      <td>...</td>\n",
       "      <td>-0.269048</td>\n",
       "      <td>0.988144</td>\n",
       "      <td>7.040028</td>\n",
       "      <td>0.347693</td>\n",
       "      <td>2.520869</td>\n",
       "      <td>2.342495</td>\n",
       "      <td>3.478175</td>\n",
       "      <td>-2.713136</td>\n",
       "      <td>10199.44</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Time         V1         V2         V3         V4          V5  \\\n",
       "46841    42951.0 -23.712839 -42.172688 -13.320825   9.925019  -13.945538   \n",
       "54018    46253.0 -21.780665 -38.305310 -12.122469   9.752791  -12.880794   \n",
       "58465    48401.0 -36.802320 -63.344698 -20.645794  16.715537  -20.672064   \n",
       "151296   95286.0 -34.549296 -60.464618 -21.340854  16.875344  -19.229075   \n",
       "169457  119713.0 -20.924897 -37.943452 -14.060281  10.473005  -10.866639   \n",
       "274771  166198.0 -35.548539 -31.850484 -48.325589  15.304184 -113.743307   \n",
       "284249  172273.0  -9.030538 -11.112584 -16.233798   3.592021  -40.427726   \n",
       "\n",
       "               V6          V7         V8        V9  ...          V21  \\\n",
       "46841    5.564891   15.710644  -2.844253 -1.580725  ...     7.921600   \n",
       "54018    4.256017   14.785051  -2.818253 -0.667338  ...     7.437478   \n",
       "58465    7.694002   24.956587  -4.730111 -2.687312  ...    11.455313   \n",
       "151296   6.335259   24.422716  -4.964566  0.188912  ...    11.502580   \n",
       "169457   6.256654   14.960521  -2.392155 -0.597076  ...     6.829810   \n",
       "274771  73.301626  120.589494 -27.347360 -3.872425  ...   -21.620120   \n",
       "284249  23.917837   44.054461  -7.277778 -4.210637  ...    -0.269048   \n",
       "\n",
       "              V22        V23       V24       V25       V26        V27  \\\n",
       "46841   -6.320710 -11.310338  0.404175 -4.547278 -1.577118  -2.357385   \n",
       "54018   -5.619439 -10.547038  0.653249 -4.232409 -0.480459  -2.257913   \n",
       "58465  -10.933144 -17.173665  1.180700 -7.025783 -2.534330  -3.602479   \n",
       "151296  -9.499423 -16.513186  0.744341 -7.081325 -2.604551  -3.550963   \n",
       "169457  -6.926353  -9.928657 -0.447084 -4.848151 -2.241620  -2.140723   \n",
       "274771   5.712303  -1.581098  4.584549  4.554683  3.415636  31.612198   \n",
       "284249   0.988144   7.040028  0.347693  2.520869  2.342495   3.478175   \n",
       "\n",
       "              V28    Amount  Class  \n",
       "46841    2.253662  12910.93      0  \n",
       "54018    2.082488  11898.09      0  \n",
       "58465    3.450224  19656.53      0  \n",
       "151296   3.250802  18910.00      0  \n",
       "169457   2.001492  11789.84      0  \n",
       "274771 -15.430084  25691.16      0  \n",
       "284249  -2.713136  10199.44      0  \n",
       "\n",
       "[7 rows x 31 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cc[cc.Amount>10000]\n",
    "cc = cc[cc.Amount<10000]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalizing the amount variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "cc['amt_normalized'] = ((cc.Amount) - (cc.Amount.mean()))/(cc.Amount.std())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Create training (67% of the data) and test (33%) data sets. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = cc.Class\n",
    "X = cc.drop(columns =['Class','Amount','Time'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Train and Test datasets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> Using logistic regression classifier to the training data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9992348609910122"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[190464    121]\n",
      " [    25    205]]\n"
     ]
    }
   ],
   "source": [
    "# instantiate a logistic regression model, and fit with X_train and y_train\n",
    "model = LogisticRegression()\n",
    "model = model.fit(X_train, y_train)\n",
    "\n",
    "# check the accuracy on the training set\n",
    "model.score(X_train, y_train)\n",
    "\n",
    "# Predict class labels for the test set\n",
    "predicted = model.predict(X_train)\n",
    "\n",
    "# Confusion Matrix for train data\n",
    "print(confusion_matrix(predicted, y_train))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confusion Matrix for <b>test</b> dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9991275110657133"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[93799    63]\n",
      " [   19   103]]\n"
     ]
    }
   ],
   "source": [
    "# check the accuracy on the test dataset\n",
    "model.score(X_test, y_test)\n",
    "\n",
    "# Predict class labels for the test dataset\n",
    "predicted = model.predict(X_test)\n",
    "\n",
    "# Confusion Matrix for test data\n",
    "print(confusion_matrix(predicted, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>A. Percision = $\\frac{TP}{TP+FP}$\n",
    "    <br>B. Recall = $\\frac{TP}{TP+FN}$\n",
    "    <br>C. F1 score = $\\frac{2}{\\frac{1}{Precision} + \\frac{1}{Recall}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00     93862\n",
      "           1       0.62      0.84      0.72       122\n",
      "\n",
      "   micro avg       1.00      1.00      1.00     93984\n",
      "   macro avg       0.81      0.92      0.86     93984\n",
      "weighted avg       1.00      1.00      1.00     93984\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(classification_report(predicted, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'ROC curve')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'FPR (Precision)')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'TPR (Recall)')"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e93b0d438>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e93b0da20>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e9381ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area under curve (AUC):  0.9705905846413216\n"
     ]
    }
   ],
   "source": [
    "#ROC, AUC\n",
    "from sklearn.metrics import roc_curve, auc\n",
    "y_score = model.predict_proba(X_test)[:,1]\n",
    "fpr, tpr, _ = roc_curve(y_test, y_score)\n",
    "\n",
    "title('ROC curve')\n",
    "xlabel('FPR (Precision)')\n",
    "ylabel('TPR (Recall)')\n",
    "\n",
    "plot(fpr,tpr)\n",
    "plot((0,1), ls='dashed',color='black')\n",
    "plt.show()\n",
    "print('Area under curve (AUC): ', auc(fpr,tpr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is highly imbalanced dataset. Because of which we are getting very high accuracy score and AUC scores.<br> Confusion matrix shows us that our model is predicting non-fradulent transactions more efficiently than the fradulent transactions (F1 score for non-fradulent transactions is 100% whereas for fradulent transactions it is 72%). <br>One reason for this is - We have 99.9% of non-fradulent transactions and only 0.172% of fradulent transactions.\n",
    "\n",
    "Objective is to correctly identify the fradulent transactions. We cannot afford to mispredict so many fradulent transactions. The model is able to predict only 62% of fraudulent transactions (precision score)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b> In order to treat imbalanced dataset, we will use oversampling method (SMOTE) to generate similar records of minority class (i.e. fradulent transactions in this dataset)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b><i>Informed Oversampling - Synthetic Minority Over-sampling Technique (SMOTE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from imblearn.over_sampling import SMOTE\n",
    "sm = SMOTE(random_state=42)\n",
    "X_res, y_res = sm.fit_resample(X_train, y_train)\n",
    "\n",
    "#  Train and Test datasets\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_res, y_res, test_size=0.33, random_state=0)\n",
    "\n",
    "# instantiate a logistic regression model, and fit with X_train and y_train\n",
    "model = LogisticRegression()\n",
    "model = model.fit(X_res, y_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9563246184071331"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[61379  3885]\n",
      " [ 1606 58853]]\n",
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       0.97      0.94      0.96     65264\n",
      "           1       0.94      0.97      0.96     60459\n",
      "\n",
      "   micro avg       0.96      0.96      0.96    125723\n",
      "   macro avg       0.96      0.96      0.96    125723\n",
      "weighted avg       0.96      0.96      0.96    125723\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# check the accuracy on the test dataset\n",
    "model.score(X_test, y_test)\n",
    "\n",
    "# Predict class labels for the test dataset\n",
    "predicted = model.predict(X_test)\n",
    "\n",
    "# Confusion Matrix for test data\n",
    "print(confusion_matrix(predicted, y_test))\n",
    "\n",
    "print(classification_report(predicted, y_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'ROC curve')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'FPR (Precision)')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'TPR (Recall)')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e939ffda0>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e93a09438>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12e92bf18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Area under curve (AUC):  0.9938563499135517\n"
     ]
    }
   ],
   "source": [
    "#ROC, AUC\n",
    "from sklearn.metrics import roc_curve, auc\n",
    "y_score = model.predict_proba(X_test)[:,1]\n",
    "fpr, tpr, _ = roc_curve(y_test, y_score)\n",
    "\n",
    "title('ROC curve')\n",
    "xlabel('FPR (Precision)')\n",
    "ylabel('TPR (Recall)')\n",
    "\n",
    "plot(fpr,tpr)\n",
    "plot((0,1), ls='dashed',color='black')\n",
    "plt.show()\n",
    "print('Area under curve (AUC): ', auc(fpr,tpr))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>After doing SMOTE (Oversampling), our AUC, precision, recall & F1 scores have increased to 99.3%, 94%, 97% & 96% respectively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------------------------------ End of document ------------------------------ "
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "HW1-CC_Fraud_Questions.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}