2_5_CreditCardFraud.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Credit Card Fraud Detection\n",
    "\n",
    "Let's try and detect credit card frauds!\n",
    "\n",
    "<img src=\"fig/credit_card_fraud.jpg\">\n",
    "\n",
    "This example is built starting from a dataset from the kaggle platform, you can find the original dataset [here](https://www.kaggle.com/mlg-ulb/creditcardfraud).\n",
    "\n",
    "The datasets contains transactions made by credit cards in September 2013 by european cardholders in two days.\n",
    "\n",
    "Given the size of the dataset (284,807 transactions), and since there since it is very unbalanced (\"only\" 492 frauds in two days), we selected a random sample of the normal transactions that we can easily work with. (You can find the code we used [here](src/creditcard/creditcard_subsamples.R))\n",
    "\n",
    "Let's import the csv file and take a look!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "source('src/lib.R')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import the data\n",
    "creditcard = read_csv('data/creditcard_15k.csv', col_types = cols())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's have a look at the data\n",
    "\n",
    "The data is composed of only numerical input variables (V1, V2, ... V28 are the result of a PCA transformation). Unfortunately, due to confidentiality issues, we do not have the original features and more background information about the data. The only original features 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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Time</th><th scope=col>V1</th><th scope=col>V2</th><th scope=col>V3</th><th scope=col>V4</th><th scope=col>V5</th><th scope=col>V6</th><th scope=col>V7</th><th scope=col>V8</th><th scope=col>V9</th><th scope=col>...</th><th scope=col>V21</th><th scope=col>V22</th><th scope=col>V23</th><th scope=col>V24</th><th scope=col>V25</th><th scope=col>V26</th><th scope=col>V27</th><th scope=col>V28</th><th scope=col>Amount</th><th scope=col>Class</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td> 26         </td><td>-0.5299123  </td><td> 0.87389158 </td><td>1.34724733  </td><td> 0.1454567  </td><td> 0.41420886 </td><td> 0.10022309 </td><td> 0.71120608 </td><td> 0.176065957</td><td>-0.28671694 </td><td>...         </td><td> 0.046949067</td><td> 0.2081049  </td><td>-0.18554835 </td><td> 0.00103066 </td><td> 0.0988157  </td><td>-0.55290360 </td><td>-0.073288084</td><td> 0.02330704 </td><td>  6.14      </td><td>0           </td></tr>\n",
       "\t<tr><td> 34         </td><td>-0.7622557  </td><td> 0.12776775 </td><td>2.65005639  </td><td>-1.8756628  </td><td>-0.89335640 </td><td>-0.26871489 </td><td>-0.41986360 </td><td> 0.146233407</td><td>-0.86963529 </td><td>...         </td><td> 0.433349642</td><td> 1.2604027  </td><td>-0.40470004 </td><td> 0.09494552 </td><td> 0.4809760  </td><td>-0.09068468 </td><td> 0.319222973</td><td> 0.13559993 </td><td> 15.99      </td><td>0           </td></tr>\n",
       "\t<tr><td> 49         </td><td> 0.9215437  </td><td>-0.06708375 </td><td>0.07746103  </td><td> 0.9536382  </td><td> 0.06741246 </td><td> 0.01615247 </td><td> 0.32045156 </td><td> 0.038534028</td><td>-0.39151266 </td><td>...         </td><td>-0.333929581</td><td>-1.2999196  </td><td> 0.08431099 </td><td>-0.37039787 </td><td> 0.1551016  </td><td>-0.83449036 </td><td> 0.000909065</td><td> 0.03554688 </td><td>135.51      </td><td>0           </td></tr>\n",
       "\t<tr><td> 51         </td><td> 1.2598731  </td><td> 0.25423958 </td><td>0.51478863  </td><td> 0.6209243  </td><td>-0.47593010 </td><td>-0.99228584 </td><td> 0.06641651 </td><td>-0.209275058</td><td> 0.03557156 </td><td>...         </td><td>-0.256530536</td><td>-0.7392117  </td><td> 0.13573238 </td><td> 0.38198987 </td><td> 0.2193019  </td><td> 0.09429069 </td><td>-0.028686668</td><td> 0.01919759 </td><td>  1.98      </td><td>0           </td></tr>\n",
       "\t<tr><td> 53         </td><td>-1.1989677  </td><td>-1.47410047 </td><td>1.84032599  </td><td>-4.5158244  </td><td> 0.32756743 </td><td>-0.17446928 </td><td> 0.95972570 </td><td>-1.026456228</td><td> 1.70043458 </td><td>...         </td><td>-0.453169417</td><td> 0.3346140  </td><td>-0.36454141 </td><td>-0.31018578 </td><td>-0.3025995  </td><td>-1.24392415 </td><td>-1.123456545</td><td>-0.73435109 </td><td> 89.17      </td><td>0           </td></tr>\n",
       "\t<tr><td>111         </td><td>-0.8208602  </td><td> 1.02256699 </td><td>1.99656036  </td><td> 1.1801408  </td><td> 0.23246391 </td><td>-0.12395255 </td><td> 0.68437085 </td><td>-0.008256437</td><td>-0.57241030 </td><td>...         </td><td> 0.000169258</td><td> 0.1833824  </td><td>-0.29991512 </td><td> 0.43180637 </td><td> 0.4567055  </td><td>-0.21329820 </td><td>-0.033160782</td><td> 0.08837199 </td><td>  9.99      </td><td>0           </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllllllllllllllllllllllllllllll}\n",
       " Time & V1 & V2 & V3 & V4 & V5 & V6 & V7 & V8 & V9 & ... & V21 & V22 & V23 & V24 & V25 & V26 & V27 & V28 & Amount & Class\\\\\n",
       "\\hline\n",
       "\t  26          & -0.5299123   &  0.87389158  & 1.34724733   &  0.1454567   &  0.41420886  &  0.10022309  &  0.71120608  &  0.176065957 & -0.28671694  & ...          &  0.046949067 &  0.2081049   & -0.18554835  &  0.00103066  &  0.0988157   & -0.55290360  & -0.073288084 &  0.02330704  &   6.14       & 0           \\\\\n",
       "\t  34          & -0.7622557   &  0.12776775  & 2.65005639   & -1.8756628   & -0.89335640  & -0.26871489  & -0.41986360  &  0.146233407 & -0.86963529  & ...          &  0.433349642 &  1.2604027   & -0.40470004  &  0.09494552  &  0.4809760   & -0.09068468  &  0.319222973 &  0.13559993  &  15.99       & 0           \\\\\n",
       "\t  49          &  0.9215437   & -0.06708375  & 0.07746103   &  0.9536382   &  0.06741246  &  0.01615247  &  0.32045156  &  0.038534028 & -0.39151266  & ...          & -0.333929581 & -1.2999196   &  0.08431099  & -0.37039787  &  0.1551016   & -0.83449036  &  0.000909065 &  0.03554688  & 135.51       & 0           \\\\\n",
       "\t  51          &  1.2598731   &  0.25423958  & 0.51478863   &  0.6209243   & -0.47593010  & -0.99228584  &  0.06641651  & -0.209275058 &  0.03557156  & ...          & -0.256530536 & -0.7392117   &  0.13573238  &  0.38198987  &  0.2193019   &  0.09429069  & -0.028686668 &  0.01919759  &   1.98       & 0           \\\\\n",
       "\t  53          & -1.1989677   & -1.47410047  & 1.84032599   & -4.5158244   &  0.32756743  & -0.17446928  &  0.95972570  & -1.026456228 &  1.70043458  & ...          & -0.453169417 &  0.3346140   & -0.36454141  & -0.31018578  & -0.3025995   & -1.24392415  & -1.123456545 & -0.73435109  &  89.17       & 0           \\\\\n",
       "\t 111          & -0.8208602   &  1.02256699  & 1.99656036   &  1.1801408   &  0.23246391  & -0.12395255  &  0.68437085  & -0.008256437 & -0.57241030  & ...          &  0.000169258 &  0.1833824   & -0.29991512  &  0.43180637  &  0.4567055   & -0.21329820  & -0.033160782 &  0.08837199  &   9.99       & 0           \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Time | V1 | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 | ... | V21 | V22 | V23 | V24 | V25 | V26 | V27 | V28 | Amount | Class | \n",
       "|---|---|---|---|---|---|\n",
       "|  26          | -0.5299123   |  0.87389158  | 1.34724733   |  0.1454567   |  0.41420886  |  0.10022309  |  0.71120608  |  0.176065957 | -0.28671694  | ...          |  0.046949067 |  0.2081049   | -0.18554835  |  0.00103066  |  0.0988157   | -0.55290360  | -0.073288084 |  0.02330704  |   6.14       | 0            | \n",
       "|  34          | -0.7622557   |  0.12776775  | 2.65005639   | -1.8756628   | -0.89335640  | -0.26871489  | -0.41986360  |  0.146233407 | -0.86963529  | ...          |  0.433349642 |  1.2604027   | -0.40470004  |  0.09494552  |  0.4809760   | -0.09068468  |  0.319222973 |  0.13559993  |  15.99       | 0            | \n",
       "|  49          |  0.9215437   | -0.06708375  | 0.07746103   |  0.9536382   |  0.06741246  |  0.01615247  |  0.32045156  |  0.038534028 | -0.39151266  | ...          | -0.333929581 | -1.2999196   |  0.08431099  | -0.37039787  |  0.1551016   | -0.83449036  |  0.000909065 |  0.03554688  | 135.51       | 0            | \n",
       "|  51          |  1.2598731   |  0.25423958  | 0.51478863   |  0.6209243   | -0.47593010  | -0.99228584  |  0.06641651  | -0.209275058 |  0.03557156  | ...          | -0.256530536 | -0.7392117   |  0.13573238  |  0.38198987  |  0.2193019   |  0.09429069  | -0.028686668 |  0.01919759  |   1.98       | 0            | \n",
       "|  53          | -1.1989677   | -1.47410047  | 1.84032599   | -4.5158244   |  0.32756743  | -0.17446928  |  0.95972570  | -1.026456228 |  1.70043458  | ...          | -0.453169417 |  0.3346140   | -0.36454141  | -0.31018578  | -0.3025995   | -1.24392415  | -1.123456545 | -0.73435109  |  89.17       | 0            | \n",
       "| 111          | -0.8208602   |  1.02256699  | 1.99656036   |  1.1801408   |  0.23246391  | -0.12395255  |  0.68437085  | -0.008256437 | -0.57241030  | ...          |  0.000169258 |  0.1833824   | -0.29991512  |  0.43180637  |  0.4567055   | -0.21329820  | -0.033160782 |  0.08837199  |   9.99       | 0            | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Time V1         V2          V3         V4         V5          V6         \n",
       "1  26  -0.5299123  0.87389158 1.34724733  0.1454567  0.41420886  0.10022309\n",
       "2  34  -0.7622557  0.12776775 2.65005639 -1.8756628 -0.89335640 -0.26871489\n",
       "3  49   0.9215437 -0.06708375 0.07746103  0.9536382  0.06741246  0.01615247\n",
       "4  51   1.2598731  0.25423958 0.51478863  0.6209243 -0.47593010 -0.99228584\n",
       "5  53  -1.1989677 -1.47410047 1.84032599 -4.5158244  0.32756743 -0.17446928\n",
       "6 111  -0.8208602  1.02256699 1.99656036  1.1801408  0.23246391 -0.12395255\n",
       "  V7          V8           V9          ... V21          V22        V23        \n",
       "1  0.71120608  0.176065957 -0.28671694 ...  0.046949067  0.2081049 -0.18554835\n",
       "2 -0.41986360  0.146233407 -0.86963529 ...  0.433349642  1.2604027 -0.40470004\n",
       "3  0.32045156  0.038534028 -0.39151266 ... -0.333929581 -1.2999196  0.08431099\n",
       "4  0.06641651 -0.209275058  0.03557156 ... -0.256530536 -0.7392117  0.13573238\n",
       "5  0.95972570 -1.026456228  1.70043458 ... -0.453169417  0.3346140 -0.36454141\n",
       "6  0.68437085 -0.008256437 -0.57241030 ...  0.000169258  0.1833824 -0.29991512\n",
       "  V24         V25        V26         V27          V28         Amount Class\n",
       "1  0.00103066  0.0988157 -0.55290360 -0.073288084  0.02330704   6.14 0    \n",
       "2  0.09494552  0.4809760 -0.09068468  0.319222973  0.13559993  15.99 0    \n",
       "3 -0.37039787  0.1551016 -0.83449036  0.000909065  0.03554688 135.51 0    \n",
       "4  0.38198987  0.2193019  0.09429069 -0.028686668  0.01919759   1.98 0    \n",
       "5 -0.31018578 -0.3025995 -1.24392415 -1.123456545 -0.73435109  89.17 0    \n",
       "6  0.43180637  0.4567055 -0.21329820 -0.033160782  0.08837199   9.99 0    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "creditcard %>% head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The column 'Class' is our label, it equals 1 in case of fraud and 0 otherwise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Class</th><th scope=col>Transactions</th><th scope=col>Average_Amount</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>0        </td><td>14508    </td><td> 89.88984</td></tr>\n",
       "\t<tr><td>1        </td><td>  492    </td><td>122.21132</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       " Class & Transactions & Average\\_Amount\\\\\n",
       "\\hline\n",
       "\t 0         & 14508     &  89.88984\\\\\n",
       "\t 1         &   492     & 122.21132\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Class | Transactions | Average_Amount | \n",
       "|---|---|\n",
       "| 0         | 14508     |  89.88984 | \n",
       "| 1         |   492     | 122.21132 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Class Transactions Average_Amount\n",
       "1 0     14508         89.88984     \n",
       "2 1       492        122.21132     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "creditcard %>% group_by(Class) %>%\n",
    "  summarise(Transactions = n(), Average_Amount = mean(Amount))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take a look at the amounts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Transactions</th><th scope=col>Average_Amount</th><th scope=col>Minimum_Amount</th><th scope=col>Maximum_Amount</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>15000   </td><td>90.94998</td><td>0       </td><td>10199.44</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llll}\n",
       " Transactions & Average\\_Amount & Minimum\\_Amount & Maximum\\_Amount\\\\\n",
       "\\hline\n",
       "\t 15000    & 90.94998 & 0        & 10199.44\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Transactions | Average_Amount | Minimum_Amount | Maximum_Amount | \n",
       "|---|\n",
       "| 15000    | 90.94998 | 0        | 10199.44 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Transactions Average_Amount Minimum_Amount Maximum_Amount\n",
       "1 15000        90.94998       0              10199.44      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "creditcard %>%\n",
    "  summarise(Transactions = n(),\n",
    "            Average_Amount = mean(Amount),\n",
    "            Minimum_Amount = min(Amount),\n",
    "            Maximum_Amount = max(Amount))\n",
    "\n",
    "options(repr.plot.width=7, repr.plot.height=3)\n",
    "creditcard %>%\n",
    "  ggplot(aes(x = Amount)) + geom_histogram(binwidth = 100) + \n",
    "  labs(title='Transaction Amounts', y='Logarithm of frequency') +\n",
    "  scale_y_log10() + xlim(c(0,10000)) #+ theme(legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlations\n",
    "\n",
    "Let's calculate the Pearson correlation for the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qMpLMxevvemVJY96jM+Y5KkCgAAmGPb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\n/wcg+8rTR41kogAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "correlations = creditcard  %>% cor(use = \"complete.obs\", method = \"pearson\")\n",
    "\n",
    "correlations[upper.tri(correlations)] = 0\n",
    "\n",
    "correlations_gathered = as.data.frame(correlations) %>% \n",
    "  mutate(Var1 = factor(row.names(.), levels=row.names(.))) %>% \n",
    "  gather(key = Var2, value = value, -Var1, na.rm = TRUE, factor_key = TRUE) \n",
    "\n",
    "options(repr.plot.width=6, repr.plot.height=6)\n",
    "ggplot(data = correlations_gathered, aes(Var2, Var1, fill = value)) + \n",
    "  geom_tile(color = \"white\")+\n",
    "  scale_fill_gradient2(low = \"blue\", high = \"red\", mid = \"white\",\n",
    "                       midpoint = 0, limit = c(-1,1), space = \"Lab\",\n",
    "                       name=\"Pearson\\nCorrelation\") +\n",
    "  theme_minimal() +\n",
    "  theme(axis.text.y = element_text(angle = 0, vjust = 1,\n",
    "                                   size = 7, hjust = 1),\n",
    "        axis.text.x = element_text(angle = 90, vjust = 1,\n",
    "                                   size = 7, hjust = 0),\n",
    "       legend.position = c(0.85, 0.3)) +\n",
    " scale_x_discrete(position = \"top\") +\n",
    " xlab('') + ylab('') +\n",
    " ggtitle('Correlation Heatmap') +\n",
    " coord_fixed()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The features are mostly not correlated (because of the PCA algorithm)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pre-processing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "## let's set up the features...\n",
    "features =\n",
    "    creditcard %>%\n",
    "    select(Time, # select features\n",
    "           V1:V28,\n",
    "           Amount) %>% \n",
    "    mutate_if(is.character, fct_explicit_na) %>% # assign levels to missing obs\n",
    "    mutate_all(as.numeric) %>% mutate_all(funs(replace(., is.na(.), 0))) %>% # set missing obs to 0\n",
    "    mutate_all(scale) # normalize data\n",
    "\n",
    "data = features\n",
    "\n",
    "## and the labels\n",
    "data$Class = creditcard$Class %>% recode('1' = 'Fraud', '0' = 'Normal') %>% factor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partitioning the data\n",
    "\n",
    "Let's partition the dataset into training and testing subsamples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train data size\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>10500</li>\n",
       "\t<li>31</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 10500\n",
       "\\item 31\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 10500\n",
       "2. 31\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 10500    31"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test data size\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>4500</li>\n",
       "\t<li>31</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 4500\n",
       "\\item 31\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 4500\n",
       "2. 31\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 4500   31"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(123)\n",
    "\n",
    "partition = data %>% nrow %>% seq_len %>% createDataPartition(times = 1, p = 0.7, list = F)\n",
    "\n",
    "train = data %>% slice(partition)\n",
    "test = data %>% slice(-partition)\n",
    "\n",
    "cat('train data size\\n')\n",
    "train %>% dim\n",
    "\n",
    "cat('test data size\\n')\n",
    "test %>% dim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting a model\n",
    "\n",
    "Let's try and fit a model!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "training started at"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1] \"2018-06-05 10:26:10 CEST\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting kmax = 5, distance = 2, kernel = optimal on full training set\n",
      "training finished at"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1] \"2018-06-05 10:26:17 CEST\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "This is the resulting model:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "k-Nearest Neighbors \n",
       "\n",
       "10500 samples\n",
       "   30 predictor\n",
       "    2 classes: 'Fraud', 'Normal' \n",
       "\n",
       "No pre-processing\n",
       "Resampling: None "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cat('training started at')\n",
    "Sys.time()\n",
    "\n",
    "#####################\n",
    "# Modify this part! #\n",
    "#####################\n",
    "model = train(x = train %>% select(-Class),\n",
    "              y = train %>% pull(Class),\n",
    "              method = 'kknn', ## how about a different model?\n",
    "              ks = 5,  ## or different hyperparameters?\n",
    "              trControl = trainControl(method = 'none', verboseIter = T)\n",
    ")\n",
    "#####################\n",
    "\n",
    "cat('training finished at')\n",
    "Sys.time()\n",
    "\n",
    "cat('\\nThis is the resulting model:\\n')\n",
    "\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How did we do?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Confusion Matrix and Statistics\n",
       "\n",
       "          Reference\n",
       "Prediction Fraud Normal\n",
       "    Fraud    139     16\n",
       "    Normal    19   4326\n",
       "                                          \n",
       "               Accuracy : 0.9922          \n",
       "                 95% CI : (0.9892, 0.9946)\n",
       "    No Information Rate : 0.9649          \n",
       "    P-Value [Acc > NIR] : <2e-16          \n",
       "                                          \n",
       "                  Kappa : 0.8842          \n",
       " Mcnemar's Test P-Value : 0.7353          \n",
       "                                          \n",
       "            Sensitivity : 0.87975         \n",
       "            Specificity : 0.99632         \n",
       "         Pos Pred Value : 0.89677         \n",
       "         Neg Pred Value : 0.99563         \n",
       "             Prevalence : 0.03511         \n",
       "         Detection Rate : 0.03089         \n",
       "   Detection Prevalence : 0.03444         \n",
       "      Balanced Accuracy : 0.93803         \n",
       "                                          \n",
       "       'Positive' Class : Fraud           \n",
       "                                          "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_response = model %>%\n",
    "  predict(newdata = test %>% select(-Class))\n",
    "\n",
    "confusionMatrix(test_response,\n",
    "                test %>% pull(Class),\n",
    "                positive = 'Fraud')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How did we really do?\n",
    "\n",
    "Since fraud detection is so unbalanced toward normal transactions, we should use the AUROC as a measure of performance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>AR:</strong> 0.88"
      ],
      "text/latex": [
       "\\textbf{AR:} 0.88"
      ],
      "text/markdown": [
       "**AR:** 0.88"
      ],
      "text/plain": [
       "  AR \n",
       "0.88 "
      ]
     },
     "metadata": {},
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   ],
   "source": [
    "roc(test_response,\n",
    "    test$Class) %>% \n",
    "    auc(.) %>% round(2)*2-1 %>% list('AR' = .) %>% unlist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now...\n",
    "\n",
    "...go back and modify the code!\n",
    "\n",
    "* How about different models/hyperparameters?\n",
    "* Given a model, can you tune its hyperparameters?\n",
    "* What about mixing two or three models with an ensemble?\n",
    "* What is the highest AUROC you can get?\n",
    "* What do you think is more important between Sensitivity and Specificity? Which would be the implications?\n",
    "    * What if we wanted to maximize Sensitivity?\n"
   ]
  }
 ],
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