Imbalanced classification: credit card fraud detection

library(keras3)
use_backend("jax")

Introduction

This example looks at the Kaggle Credit Card Fraud Detection dataset to demonstrate how to train a classification model on data with highly imbalanced classes. You can download the data by clicking “Download” at the link, or if you’re setup with a kaggle API key at "~/.kaggle/kagle.json", you can run the following:

reticulate::py_install("kaggle", pip = TRUE)
reticulate::py_available(TRUE) # ensure 'kaggle' is on the PATH
system("kaggle datasets download -d mlg-ulb/creditcardfraud")
zip::unzip("creditcardfraud.zip", files = "creditcard.csv")

First, load the data

library(readr)
df <- read_csv("creditcard.csv", col_types = cols(
  Class = col_integer(),
  .default = col_double()
))
tibble::glimpse(df)

## Rows: 284,807
## Columns: 31
## $ Time   <dbl> 0, 0, 1, 1, 2, 2, 4, 7, 7, 9, 10, 10, 10, 11, 12, 12, 12, 1…
## $ V1     <dbl> -1.3598071, 1.1918571, -1.3583541, -0.9662717, -1.1582331, …
## $ V2     <dbl> -0.07278117, 0.26615071, -1.34016307, -0.18522601, 0.877736…
## $ V3     <dbl> 2.53634674, 0.16648011, 1.77320934, 1.79299334, 1.54871785,…
## $ V4     <dbl> 1.37815522, 0.44815408, 0.37977959, -0.86329128, 0.40303393…
## $ V5     <dbl> -0.33832077, 0.06001765, -0.50319813, -0.01030888, -0.40719…
## $ V6     <dbl> 0.46238778, -0.08236081, 1.80049938, 1.24720317, 0.09592146…
## $ V7     <dbl> 0.239598554, -0.078802983, 0.791460956, 0.237608940, 0.5929…
## $ V8     <dbl> 0.098697901, 0.085101655, 0.247675787, 0.377435875, -0.2705…
## $ V9     <dbl> 0.3637870, -0.2554251, -1.5146543, -1.3870241, 0.8177393, -…
## $ V10    <dbl> 0.09079417, -0.16697441, 0.20764287, -0.05495192, 0.7530744…
## $ V11    <dbl> -0.55159953, 1.61272666, 0.62450146, -0.22648726, -0.822842…
## $ V12    <dbl> -0.61780086, 1.06523531, 0.06608369, 0.17822823, 0.53819555…
## $ V13    <dbl> -0.99138985, 0.48909502, 0.71729273, 0.50775687, 1.34585159…
## $ V14    <dbl> -0.31116935, -0.14377230, -0.16594592, -0.28792375, -1.1196…
## $ V15    <dbl> 1.468176972, 0.635558093, 2.345864949, -0.631418118, 0.1751…
## $ V16    <dbl> -0.47040053, 0.46391704, -2.89008319, -1.05964725, -0.45144…
## $ V17    <dbl> 0.207971242, -0.114804663, 1.109969379, -0.684092786, -0.23…
## $ V18    <dbl> 0.02579058, -0.18336127, -0.12135931, 1.96577500, -0.038194…
## $ V19    <dbl> 0.40399296, -0.14578304, -2.26185710, -1.23262197, 0.803486…
## $ V20    <dbl> 0.25141210, -0.06908314, 0.52497973, -0.20803778, 0.4085423…
## $ V21    <dbl> -0.018306778, -0.225775248, 0.247998153, -0.108300452, -0.0…
## $ V22    <dbl> 0.277837576, -0.638671953, 0.771679402, 0.005273597, 0.7982…
## $ V23    <dbl> -0.110473910, 0.101288021, 0.909412262, -0.190320519, -0.13…
## $ V24    <dbl> 0.06692807, -0.33984648, -0.68928096, -1.17557533, 0.141266…
## $ V25    <dbl> 0.12853936, 0.16717040, -0.32764183, 0.64737603, -0.2060095…
## $ V26    <dbl> -0.18911484, 0.12589453, -0.13909657, -0.22192884, 0.502292…
## $ V27    <dbl> 0.133558377, -0.008983099, -0.055352794, 0.062722849, 0.219…
## $ V28    <dbl> -0.021053053, 0.014724169, -0.059751841, 0.061457629, 0.215…
## $ Amount <dbl> 149.62, 2.69, 378.66, 123.50, 69.99, 3.67, 4.99, 40.80, 93.…
## $ Class  <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…

Prepare a validation set

val_idx <- nrow(df) %>% sample.int(., round( . * 0.2))
val_df <- df[val_idx, ]
train_df <- df[-val_idx, ]

cat("Number of training samples:", nrow(train_df), "\n")

## Number of training samples: 227846

cat("Number of validation samples:", nrow(val_df), "\n")

## Number of validation samples: 56961

Analyze class imbalance in the targets

counts <- table(train_df$Class)
counts

##
##      0      1
## 227462    384

cat(sprintf("Number of positive samples in training data: %i (%.2f%% of total)",
            counts["1"], 100 * counts["1"] / sum(counts)))

## Number of positive samples in training data: 384 (0.17% of total)

weight_for_0 = 1 / counts["0"]
weight_for_1 = 1 / counts["1"]

Normalize the data using training set statistics

feature_names <- colnames(train_df) %>% setdiff("Class")

train_features <- as.matrix(train_df[feature_names])
train_targets <- as.matrix(train_df$Class)

val_features <- as.matrix(val_df[feature_names])
val_targets <- as.matrix(val_df$Class)

train_features %<>% scale()
val_features %<>% scale(center = attr(train_features, "scaled:center"),
                        scale = attr(train_features, "scaled:scale"))

Build a binary classification model

model <-
  keras_model_sequential(input_shape = ncol(train_features)) |>
  layer_dense(256, activation = "relu") |>
  layer_dense(256, activation = "relu") |>
  layer_dropout(0.3) |>
  layer_dense(256, activation = "relu") |>
  layer_dropout(0.3) |>
  layer_dense(1, activation = "sigmoid")

model

## Model: "sequential"
## ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━┓
## ┃ Layer (type)                    ┃ Output Shape           ┃       Param # ┃
## ┡━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━┩
## │ dense_3 (Dense)                 │ (None, 256)            │         7,936 │
## ├─────────────────────────────────┼────────────────────────┼───────────────┤
## │ dense_2 (Dense)                 │ (None, 256)            │        65,792 │
## ├─────────────────────────────────┼────────────────────────┼───────────────┤
## │ dropout_1 (Dropout)             │ (None, 256)            │             0 │
## ├─────────────────────────────────┼────────────────────────┼───────────────┤
## │ dense_1 (Dense)                 │ (None, 256)            │        65,792 │
## ├─────────────────────────────────┼────────────────────────┼───────────────┤
## │ dropout (Dropout)               │ (None, 256)            │             0 │
## ├─────────────────────────────────┼────────────────────────┼───────────────┤
## │ dense (Dense)                   │ (None, 1)              │           257 │
## └─────────────────────────────────┴────────────────────────┴───────────────┘
##  Total params: 139,777 (546.00 KB)
##  Trainable params: 139,777 (546.00 KB)
##  Non-trainable params: 0 (0.00 B)

Train the model with `class_weight` argument

metrics <- list(
  metric_false_negatives(name = "fn"),
  metric_false_positives(name = "fp"),
  metric_true_negatives(name = "tn"),
  metric_true_positives(name = "tp"),
  metric_precision(name = "precision"),
  metric_recall(name = "recall")
)
model |> compile(
  optimizer = optimizer_adam(1e-2),
  loss = "binary_crossentropy",
  metrics = metrics
)
callbacks <- list(
  callback_model_checkpoint("fraud_model_at_epoch_{epoch}.keras")
)

class_weight <- list("0" = weight_for_0,
                     "1" = weight_for_1)

model |> fit(
  train_features, train_targets,
  validation_data = list(val_features, val_targets),
  class_weight = class_weight,
  batch_size = 2048,
  epochs = 30,
  callbacks = callbacks,
  verbose = 2
)

## Epoch 1/30
## 112/112 - 3s - 22ms/step - fn: 40.0000 - fp: 24201.0000 - loss: 2.1046e-06 - precision: 0.0140 - recall: 0.8958 - tn: 203261.0000 - tp: 344.0000 - val_fn: 14.0000 - val_fp: 3327.0000 - val_loss: 0.2038 - val_precision: 0.0275 - val_recall: 0.8704 - val_tn: 53526.0000 - val_tp: 94.0000
## Epoch 2/30
## 112/112 - 0s - 4ms/step - fn: 28.0000 - fp: 8249.0000 - loss: 1.2774e-06 - precision: 0.0414 - recall: 0.9271 - tn: 219213.0000 - tp: 356.0000 - val_fn: 15.0000 - val_fp: 1896.0000 - val_loss: 0.1072 - val_precision: 0.0468 - val_recall: 0.8611 - val_tn: 54957.0000 - val_tp: 93.0000
## Epoch 3/30
## 112/112 - 0s - 2ms/step - fn: 20.0000 - fp: 6617.0000 - loss: 9.6224e-07 - precision: 0.0521 - recall: 0.9479 - tn: 220845.0000 - tp: 364.0000 - val_fn: 13.0000 - val_fp: 3453.0000 - val_loss: 0.1746 - val_precision: 0.0268 - val_recall: 0.8796 - val_tn: 53400.0000 - val_tp: 95.0000
## Epoch 4/30
## 112/112 - 0s - 2ms/step - fn: 18.0000 - fp: 7294.0000 - loss: 9.3023e-07 - precision: 0.0478 - recall: 0.9531 - tn: 220168.0000 - tp: 366.0000 - val_fn: 17.0000 - val_fp: 660.0000 - val_loss: 0.0478 - val_precision: 0.1212 - val_recall: 0.8426 - val_tn: 56193.0000 - val_tp: 91.0000
## Epoch 5/30
## 112/112 - 0s - 2ms/step - fn: 15.0000 - fp: 6663.0000 - loss: 7.2354e-07 - precision: 0.0525 - recall: 0.9609 - tn: 220799.0000 - tp: 369.0000 - val_fn: 19.0000 - val_fp: 760.0000 - val_loss: 0.0601 - val_precision: 0.1048 - val_recall: 0.8241 - val_tn: 56093.0000 - val_tp: 89.0000
## Epoch 6/30
## 112/112 - 0s - 2ms/step - fn: 16.0000 - fp: 7958.0000 - loss: 7.6664e-07 - precision: 0.0442 - recall: 0.9583 - tn: 219504.0000 - tp: 368.0000 - val_fn: 14.0000 - val_fp: 3309.0000 - val_loss: 0.1274 - val_precision: 0.0276 - val_recall: 0.8704 - val_tn: 53544.0000 - val_tp: 94.0000
## Epoch 7/30
## 112/112 - 0s - 2ms/step - fn: 17.0000 - fp: 7064.0000 - loss: 7.6301e-07 - precision: 0.0494 - recall: 0.9557 - tn: 220398.0000 - tp: 367.0000 - val_fn: 10.0000 - val_fp: 5697.0000 - val_loss: 0.2665 - val_precision: 0.0169 - val_recall: 0.9074 - val_tn: 51156.0000 - val_tp: 98.0000
## Epoch 8/30
## 112/112 - 0s - 2ms/step - fn: 14.0000 - fp: 7286.0000 - loss: 7.0213e-07 - precision: 0.0483 - recall: 0.9635 - tn: 220176.0000 - tp: 370.0000 - val_fn: 15.0000 - val_fp: 2301.0000 - val_loss: 0.0911 - val_precision: 0.0388 - val_recall: 0.8611 - val_tn: 54552.0000 - val_tp: 93.0000
## Epoch 9/30
## 112/112 - 0s - 2ms/step - fn: 18.0000 - fp: 10285.0000 - loss: 1.0564e-06 - precision: 0.0344 - recall: 0.9531 - tn: 217177.0000 - tp: 366.0000 - val_fn: 17.0000 - val_fp: 1831.0000 - val_loss: 0.0865 - val_precision: 0.0473 - val_recall: 0.8426 - val_tn: 55022.0000 - val_tp: 91.0000
## Epoch 10/30
## 112/112 - 0s - 2ms/step - fn: 15.0000 - fp: 6163.0000 - loss: 6.8741e-07 - precision: 0.0565 - recall: 0.9609 - tn: 221299.0000 - tp: 369.0000 - val_fn: 16.0000 - val_fp: 1289.0000 - val_loss: 0.0596 - val_precision: 0.0666 - val_recall: 0.8519 - val_tn: 55564.0000 - val_tp: 92.0000
## Epoch 11/30
## 112/112 - 0s - 2ms/step - fn: 13.0000 - fp: 6784.0000 - loss: 5.9445e-07 - precision: 0.0519 - recall: 0.9661 - tn: 220678.0000 - tp: 371.0000 - val_fn: 15.0000 - val_fp: 1634.0000 - val_loss: 0.0654 - val_precision: 0.0539 - val_recall: 0.8611 - val_tn: 55219.0000 - val_tp: 93.0000
## Epoch 12/30
## 112/112 - 0s - 2ms/step - fn: 8.0000 - fp: 6189.0000 - loss: 5.2899e-07 - precision: 0.0573 - recall: 0.9792 - tn: 221273.0000 - tp: 376.0000 - val_fn: 16.0000 - val_fp: 1274.0000 - val_loss: 0.0567 - val_precision: 0.0673 - val_recall: 0.8519 - val_tn: 55579.0000 - val_tp: 92.0000
## Epoch 13/30
## 112/112 - 0s - 2ms/step - fn: 6.0000 - fp: 3787.0000 - loss: 3.5831e-07 - precision: 0.0908 - recall: 0.9844 - tn: 223675.0000 - tp: 378.0000 - val_fn: 16.0000 - val_fp: 913.0000 - val_loss: 0.0410 - val_precision: 0.0915 - val_recall: 0.8519 - val_tn: 55940.0000 - val_tp: 92.0000
## Epoch 14/30
## 112/112 - 0s - 2ms/step - fn: 5.0000 - fp: 4968.0000 - loss: 4.0142e-07 - precision: 0.0709 - recall: 0.9870 - tn: 222494.0000 - tp: 379.0000 - val_fn: 16.0000 - val_fp: 1187.0000 - val_loss: 0.0526 - val_precision: 0.0719 - val_recall: 0.8519 - val_tn: 55666.0000 - val_tp: 92.0000
## Epoch 15/30
## 112/112 - 0s - 2ms/step - fn: 1.0000 - fp: 3587.0000 - loss: 2.8496e-07 - precision: 0.0965 - recall: 0.9974 - tn: 223875.0000 - tp: 383.0000 - val_fn: 17.0000 - val_fp: 1361.0000 - val_loss: 0.0620 - val_precision: 0.0627 - val_recall: 0.8426 - val_tn: 55492.0000 - val_tp: 91.0000
## Epoch 16/30
## 112/112 - 0s - 2ms/step - fn: 4.0000 - fp: 4570.0000 - loss: 3.4124e-07 - precision: 0.0768 - recall: 0.9896 - tn: 222892.0000 - tp: 380.0000 - val_fn: 17.0000 - val_fp: 771.0000 - val_loss: 0.0394 - val_precision: 0.1056 - val_recall: 0.8426 - val_tn: 56082.0000 - val_tp: 91.0000
## Epoch 17/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 3173.0000 - loss: 2.7646e-07 - precision: 0.1072 - recall: 0.9922 - tn: 224289.0000 - tp: 381.0000 - val_fn: 18.0000 - val_fp: 746.0000 - val_loss: 0.0345 - val_precision: 0.1077 - val_recall: 0.8333 - val_tn: 56107.0000 - val_tp: 90.0000
## Epoch 18/30
## 112/112 - 0s - 2ms/step - fn: 4.0000 - fp: 3197.0000 - loss: 2.5855e-07 - precision: 0.1062 - recall: 0.9896 - tn: 224265.0000 - tp: 380.0000 - val_fn: 16.0000 - val_fp: 530.0000 - val_loss: 0.0302 - val_precision: 0.1479 - val_recall: 0.8519 - val_tn: 56323.0000 - val_tp: 92.0000
## Epoch 19/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 2411.0000 - loss: 2.3853e-07 - precision: 0.1365 - recall: 0.9922 - tn: 225051.0000 - tp: 381.0000 - val_fn: 16.0000 - val_fp: 1123.0000 - val_loss: 0.0583 - val_precision: 0.0757 - val_recall: 0.8519 - val_tn: 55730.0000 - val_tp: 92.0000
## Epoch 20/30
## 112/112 - 0s - 2ms/step - fn: 5.0000 - fp: 5929.0000 - loss: 4.8075e-07 - precision: 0.0601 - recall: 0.9870 - tn: 221533.0000 - tp: 379.0000 - val_fn: 16.0000 - val_fp: 1188.0000 - val_loss: 0.0572 - val_precision: 0.0719 - val_recall: 0.8519 - val_tn: 55665.0000 - val_tp: 92.0000
## Epoch 21/30
## 112/112 - 0s - 2ms/step - fn: 4.0000 - fp: 2963.0000 - loss: 2.7795e-07 - precision: 0.1137 - recall: 0.9896 - tn: 224499.0000 - tp: 380.0000 - val_fn: 15.0000 - val_fp: 1362.0000 - val_loss: 0.0662 - val_precision: 0.0639 - val_recall: 0.8611 - val_tn: 55491.0000 - val_tp: 93.0000
## Epoch 22/30
## 112/112 - 0s - 2ms/step - fn: 4.0000 - fp: 5019.0000 - loss: 4.0863e-07 - precision: 0.0704 - recall: 0.9896 - tn: 222443.0000 - tp: 380.0000 - val_fn: 16.0000 - val_fp: 1039.0000 - val_loss: 0.0373 - val_precision: 0.0813 - val_recall: 0.8519 - val_tn: 55814.0000 - val_tp: 92.0000
## Epoch 23/30
## 112/112 - 0s - 2ms/step - fn: 2.0000 - fp: 4786.0000 - loss: 3.4249e-07 - precision: 0.0739 - recall: 0.9948 - tn: 222676.0000 - tp: 382.0000 - val_fn: 17.0000 - val_fp: 2260.0000 - val_loss: 0.0826 - val_precision: 0.0387 - val_recall: 0.8426 - val_tn: 54593.0000 - val_tp: 91.0000
## Epoch 24/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 4408.0000 - loss: 3.0581e-07 - precision: 0.0796 - recall: 0.9922 - tn: 223054.0000 - tp: 381.0000 - val_fn: 16.0000 - val_fp: 637.0000 - val_loss: 0.0328 - val_precision: 0.1262 - val_recall: 0.8519 - val_tn: 56216.0000 - val_tp: 92.0000
## Epoch 25/30
## 112/112 - 0s - 2ms/step - fn: 2.0000 - fp: 3021.0000 - loss: 2.2939e-07 - precision: 0.1123 - recall: 0.9948 - tn: 224441.0000 - tp: 382.0000 - val_fn: 17.0000 - val_fp: 653.0000 - val_loss: 0.0349 - val_precision: 0.1223 - val_recall: 0.8426 - val_tn: 56200.0000 - val_tp: 91.0000
## Epoch 26/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 2628.0000 - loss: 2.1400e-07 - precision: 0.1266 - recall: 0.9922 - tn: 224834.0000 - tp: 381.0000 - val_fn: 18.0000 - val_fp: 669.0000 - val_loss: 0.0359 - val_precision: 0.1186 - val_recall: 0.8333 - val_tn: 56184.0000 - val_tp: 90.0000
## Epoch 27/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 2728.0000 - loss: 2.2770e-07 - precision: 0.1225 - recall: 0.9922 - tn: 224734.0000 - tp: 381.0000 - val_fn: 18.0000 - val_fp: 995.0000 - val_loss: 0.0516 - val_precision: 0.0829 - val_recall: 0.8333 - val_tn: 55858.0000 - val_tp: 90.0000
## Epoch 28/30
## 112/112 - 0s - 2ms/step - fn: 1.0000 - fp: 2810.0000 - loss: 2.2002e-07 - precision: 0.1199 - recall: 0.9974 - tn: 224652.0000 - tp: 383.0000 - val_fn: 16.0000 - val_fp: 387.0000 - val_loss: 0.0241 - val_precision: 0.1921 - val_recall: 0.8519 - val_tn: 56466.0000 - val_tp: 92.0000
## Epoch 29/30
## 112/112 - 0s - 2ms/step - fn: 2.0000 - fp: 3517.0000 - loss: 3.5872e-07 - precision: 0.0980 - recall: 0.9948 - tn: 223945.0000 - tp: 382.0000 - val_fn: 19.0000 - val_fp: 365.0000 - val_loss: 0.0267 - val_precision: 0.1960 - val_recall: 0.8241 - val_tn: 56488.0000 - val_tp: 89.0000
## Epoch 30/30
## 112/112 - 0s - 2ms/step - fn: 3.0000 - fp: 3709.0000 - loss: 3.3721e-07 - precision: 0.0932 - recall: 0.9922 - tn: 223753.0000 - tp: 381.0000 - val_fn: 18.0000 - val_fp: 702.0000 - val_loss: 0.0342 - val_precision: 0.1136 - val_recall: 0.8333 - val_tn: 56151.0000 - val_tp: 90.0000

val_pred <- model %>%
  predict(val_features) %>%
  { as.integer(. > 0.5) }

## 1781/1781 - 1s - 281us/step

pred_correct <- val_df$Class == val_pred
cat(sprintf("Validation accuracy: %.2f", mean(pred_correct)))

## Validation accuracy: 0.99

fraudulent <- val_df$Class == 1

n_fraudulent_detected <- sum(fraudulent & pred_correct)
n_fraudulent_missed <- sum(fraudulent & !pred_correct)
n_legitimate_flagged <- sum(!fraudulent & !pred_correct)

Conclusions

At the end of training, out of 56,961 validation transactions, we are:

Correctly identifying 90 of them as fraudulent
Missing 18 fraudulent transactions
At the cost of incorrectly flagging 702 legitimate transactions

In the real world, one would put an even higher weight on class 1, so as to reflect that False Negatives are more costly than False Positives.

Next time your credit card gets declined in an online purchase – this is why.