Classification on imbalanced data

This tutorial demonstrates how to classify a highly imbalanced dataset in which the number of examples in one class greatly outnumbers the examples in another. You will work with the Credit Card Fraud Detection dataset hosted on Kaggle. The aim is to detect a mere 492 fraudulent transactions from 284,807 transactions in total. You will use Keras to define the model and class weights to help the model learn from the imbalanced data. .

This tutorial contains complete code to:

• Load a CSV file using Pandas.
• Create train, validation, and test sets.
• Define and train a model using Keras (including setting class weights).
• Evaluate the model using various metrics (including precision and recall).
• Try common techniques for dealing with imbalanced data like:
  • Class weighting
  • Oversampling

Setup

import tensorflow as tf
from tensorflow import keras

import os
import tempfile

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

import sklearn
from sklearn.metrics import confusion_matrix
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

2022-12-14 02:48:09.410091: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvinfer.so.7: cannot open shared object file: No such file or directory
2022-12-14 02:48:09.410192: W tensorflow/compiler/xla/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvinfer_plugin.so.7: cannot open shared object file: No such file or directory
2022-12-14 02:48:09.410202: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.

mpl.rcParams['figure.figsize'] = (12, 10)
colors = plt.rcParams['axes.prop_cycle'].by_key()['color']

Data processing and exploration

Download the Kaggle Credit Card Fraud data set

Pandas is a Python library with many helpful utilities for loading and working with structured data. It can be used to download CSVs into a Pandas DataFrame.

Note: This dataset has been collected and analysed during a research collaboration of Worldline and the Machine Learning Group of ULB (Université Libre de Bruxelles) on big data mining and fraud detection. More details on current and past projects on related topics are available here and the page of the DefeatFraud project

file = tf.keras.utils
raw_df = pd.read_csv('https://storage.googleapis.com/download.tensorflow.org/data/creditcard.csv')
raw_df.head()

raw_df[['Time', 'V1', 'V2', 'V3', 'V4', 'V5', 'V26', 'V27', 'V28', 'Amount', 'Class']].describe()

Examine the class label imbalance

Let's look at the dataset imbalance:

neg, pos = np.bincount(raw_df['Class'])
total = neg + pos
print('Examples:\n    Total: {}\n    Positive: {} ({:.2f}% of total)\n'.format(
    total, pos, 100 * pos / total))

Examples:
    Total: 284807
    Positive: 492 (0.17% of total)

This shows the small fraction of positive samples.

Clean, split and normalize the data

The raw data has a few issues. First the Time and Amount columns are too variable to use directly. Drop the Time column (since it's not clear what it means) and take the log of the Amount column to reduce its range.

cleaned_df = raw_df.copy()

# You don't want the `Time` column.
cleaned_df.pop('Time')

# The `Amount` column covers a huge range. Convert to log-space.
eps = 0.001 # 0 => 0.1¢
cleaned_df['Log Amount'] = np.log(cleaned_df.pop('Amount')+eps)

Split the dataset into train, validation, and test sets. The validation set is used during the model fitting to evaluate the loss and any metrics, however the model is not fit with this data. The test set is completely unused during the training phase and is only used at the end to evaluate how well the model generalizes to new data. This is especially important with imbalanced datasets where overfitting is a significant concern from the lack of training data.

# Use a utility from sklearn to split and shuffle your dataset.
train_df, test_df = train_test_split(cleaned_df, test_size=0.2)
train_df, val_df = train_test_split(train_df, test_size=0.2)

# Form np arrays of labels and features.
train_labels = np.array(train_df.pop('Class'))
bool_train_labels = train_labels != 0
val_labels = np.array(val_df.pop('Class'))
test_labels = np.array(test_df.pop('Class'))

train_features = np.array(train_df)
val_features = np.array(val_df)
test_features = np.array(test_df)

Normalize the input features using the sklearn StandardScaler. This will set the mean to 0 and standard deviation to 1.

Note: The StandardScaler is only fit using the train_features to be sure the model is not peeking at the validation or test sets.

scaler = StandardScaler()
train_features = scaler.fit_transform(train_features)

val_features = scaler.transform(val_features)
test_features = scaler.transform(test_features)

train_features = np.clip(train_features, -5, 5)
val_features = np.clip(val_features, -5, 5)
test_features = np.clip(test_features, -5, 5)


print('Training labels shape:', train_labels.shape)
print('Validation labels shape:', val_labels.shape)
print('Test labels shape:', test_labels.shape)

print('Training features shape:', train_features.shape)
print('Validation features shape:', val_features.shape)
print('Test features shape:', test_features.shape)

Training labels shape: (182276,)
Validation labels shape: (45569,)
Test labels shape: (56962,)
Training features shape: (182276, 29)
Validation features shape: (45569, 29)
Test features shape: (56962, 29)

Caution: If you want to deploy a model, it's critical that you preserve the preprocessing calculations. The easiest way to implement them as layers, and attach them to your model before export.

Look at the data distribution

Next compare the distributions of the positive and negative examples over a few features. Good questions to ask yourself at this point are:

• Do these distributions make sense?
  • Yes. You've normalized the input and these are mostly concentrated in the +/- 2 range.
• Can you see the difference between the distributions?
  • Yes the positive examples contain a much higher rate of extreme values.

pos_df = pd.DataFrame(train_features[ bool_train_labels], columns=train_df.columns)
neg_df = pd.DataFrame(train_features[~bool_train_labels], columns=train_df.columns)

sns.jointplot(x=pos_df['V5'], y=pos_df['V6'],
              kind='hex', xlim=(-5,5), ylim=(-5,5))
plt.suptitle("Positive distribution")

sns.jointplot(x=neg_df['V5'], y=neg_df['V6'],
              kind='hex', xlim=(-5,5), ylim=(-5,5))
_ = plt.suptitle("Negative distribution")

Define the model and metrics

Define a function that creates a simple neural network with a densly connected hidden layer, a dropout layer to reduce overfitting, and an output sigmoid layer that returns the probability of a transaction being fraudulent:

METRICS = [
      keras.metrics.TruePositives(name='tp'),
      keras.metrics.FalsePositives(name='fp'),
      keras.metrics.TrueNegatives(name='tn'),
      keras.metrics.FalseNegatives(name='fn'), 
      keras.metrics.BinaryAccuracy(name='accuracy'),
      keras.metrics.Precision(name='precision'),
      keras.metrics.Recall(name='recall'),
      keras.metrics.AUC(name='auc'),
      keras.metrics.AUC(name='prc', curve='PR'), # precision-recall curve
]

def make_model(metrics=METRICS, output_bias=None):
  if output_bias is not None:
    output_bias = tf.keras.initializers.Constant(output_bias)
  model = keras.Sequential([
      keras.layers.Dense(
          16, activation='relu',
          input_shape=(train_features.shape[-1],)),
      keras.layers.Dropout(0.5),
      keras.layers.Dense(1, activation='sigmoid',
                         bias_initializer=output_bias),
  ])

  model.compile(
      optimizer=keras.optimizers.Adam(learning_rate=1e-3),
      loss=keras.losses.BinaryCrossentropy(),
      metrics=metrics)

  return model

Understanding useful metrics

Notice that there are a few metrics defined above that can be computed by the model that will be helpful when evaluating the performance.

• False negatives and false positives are samples that were incorrectly classified
• True negatives and true positives are samples that were correctly classified
• Accuracy is the percentage of examples correctly classified > \(\frac{\text{true samples} }{\text{total samples} }\)
• Precision is the percentage of predicted positives that were correctly classified > \(\frac{\text{true positives} }{\text{true positives + false positives} }\)
• Recall is the percentage of actual positives that were correctly classified > \(\frac{\text{true positives} }{\text{true positives + false negatives} }\)
• AUC refers to the Area Under the Curve of a Receiver Operating Characteristic curve (ROC-AUC). This metric is equal to the probability that a classifier will rank a random positive sample higher than a random negative sample.
• AUPRC refers to Area Under the Curve of the Precision-Recall Curve. This metric computes precision-recall pairs for different probability thresholds.

Note: Accuracy is not a helpful metric for this task. You can have 99.8%+ accuracy on this task by predicting False all the time.

Read more:

• True vs. False and Positive vs. Negative
• Accuracy
• Precision and Recall
• ROC-AUC
• Relationship between Precision-Recall and ROC Curves

Baseline model

Build the model

Now create and train your model using the function that was defined earlier. Notice that the model is fit using a larger than default batch size of 2048, this is important to ensure that each batch has a decent chance of containing a few positive samples. If the batch size was too small, they would likely have no fraudulent transactions to learn from.

Note: this model will not handle the class imbalance well. You will improve it later in this tutorial.

EPOCHS = 100
BATCH_SIZE = 2048

early_stopping = tf.keras.callbacks.EarlyStopping(
    monitor='val_prc', 
    verbose=1,
    patience=10,
    mode='max',
    restore_best_weights=True)

model = make_model()
model.summary()

Model: "sequential"
_________________________________________________________________
 Layer (type)                Output Shape              Param #   
=================================================================
 dense (Dense)               (None, 16)                480       
                                                                 
 dropout (Dropout)           (None, 16)                0         
                                                                 
 dense_1 (Dense)             (None, 1)                 17        
                                                                 
=================================================================
Total params: 497
Trainable params: 497
Non-trainable params: 0
_________________________________________________________________

Test run the model:

model.predict(train_features[:10])

1/1 [==============================] - 0s 427ms/step
array([[0.12086625],
       [0.37875205],
       [0.14548904],
       [0.1107088 ],
       [0.11098117],
       [0.13489977],
       [0.09975273],
       [0.17781098],
       [0.09235804],
       [0.176774  ]], dtype=float32)

Optional: Set the correct initial bias.

These initial guesses are not great. You know the dataset is imbalanced. Set the output layer's bias to reflect that (See: A Recipe for Training Neural Networks: "init well"). This can help with initial convergence.

With the default bias initialization the loss should be about math.log(2) = 0.69314

results = model.evaluate(train_features, train_labels, batch_size=BATCH_SIZE, verbose=0)
print("Loss: {:0.4f}".format(results[0]))

Loss: 0.1652

The correct bias to set can be derived from:

\[ p_0 = pos/(pos + neg) = 1/(1+e^{-b_0}) \]

\[ b_0 = -log_e(1/p_0 - 1) \]

\[ b_0 = log_e(pos/neg)\]

initial_bias = np.log([pos/neg])
initial_bias

array([-6.35935934])

Set that as the initial bias, and the model will give much more reasonable initial guesses.

It should be near: pos/total = 0.0018

model = make_model(output_bias=initial_bias)
model.predict(train_features[:10])

1/1 [==============================] - 0s 50ms/step
array([[0.00110731],
       [0.00280909],
       [0.00413586],
       [0.00342205],
       [0.00166295],
       [0.00368322],
       [0.00099343],
       [0.00190527],
       [0.00081247],
       [0.00266587]], dtype=float32)

With this initialization the initial loss should be approximately:

\[-p_0log(p_0)-(1-p_0)log(1-p_0) = 0.01317\]

results = model.evaluate(train_features, train_labels, batch_size=BATCH_SIZE, verbose=0)
print("Loss: {:0.4f}".format(results[0]))

Loss: 0.0101

This initial loss is about 50 times less than if would have been with naive initialization.

This way the model doesn't need to spend the first few epochs just learning that positive examples are unlikely. This also makes it easier to read plots of the loss during training.

Checkpoint the initial weights

To make the various training runs more comparable, keep this initial model's weights in a checkpoint file, and load them into each model before training:

initial_weights = os.path.join(tempfile.mkdtemp(), 'initial_weights')
model.save_weights(initial_weights)

Confirm that the bias fix helps

Before moving on, confirm quick that the careful bias initialization actually helped.

Train the model for 20 epochs, with and without this careful initialization, and compare the losses:

model = make_model()
model.load_weights(initial_weights)
model.layers[-1].bias.assign([0.0])
zero_bias_history = model.fit(
    train_features,
    train_labels,
    batch_size=BATCH_SIZE,
    epochs=20,
    validation_data=(val_features, val_labels), 
    verbose=0)

model = make_model()
model.load_weights(initial_weights)
careful_bias_history = model.fit(
    train_features,
    train_labels,
    batch_size=BATCH_SIZE,
    epochs=20,
    validation_data=(val_features, val_labels), 
    verbose=0)

def plot_loss(history, label, n):
  # Use a log scale on y-axis to show the wide range of values.
  plt.semilogy(history.epoch, history.history['loss'],
               color=colors[n], label='Train ' + label)
  plt.semilogy(history.epoch, history.history['val_loss'],
               color=colors[n], label='Val ' + label,
               linestyle="--")
  plt.xlabel('Epoch')
  plt.ylabel('Loss')

plot_loss(zero_bias_history, "Zero Bias", 0)
plot_loss(careful_bias_history, "Careful Bias", 1)

The above figure makes it clear: In terms of validation loss, on this problem, this careful initialization gives a clear advantage.

Train the model

model = make_model()
model.load_weights(initial_weights)
baseline_history = model.fit(
    train_features,
    train_labels,
    batch_size=BATCH_SIZE,
    epochs=EPOCHS,
    callbacks=[early_stopping],
    validation_data=(val_features, val_labels))

Epoch 1/100
90/90 [==============================] - 2s 11ms/step - loss: 0.0108 - tp: 156.0000 - fp: 138.0000 - tn: 227312.0000 - fn: 239.0000 - accuracy: 0.9983 - precision: 0.5306 - recall: 0.3949 - auc: 0.8656 - prc: 0.3547 - val_loss: 0.0055 - val_tp: 44.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 37.0000 - val_accuracy: 0.9990 - val_precision: 0.8462 - val_recall: 0.5432 - val_auc: 0.9051 - val_prc: 0.6984
Epoch 2/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0067 - tp: 153.0000 - fp: 34.0000 - tn: 181928.0000 - fn: 161.0000 - accuracy: 0.9989 - precision: 0.8182 - recall: 0.4873 - auc: 0.9011 - prc: 0.5735 - val_loss: 0.0048 - val_tp: 49.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 32.0000 - val_accuracy: 0.9991 - val_precision: 0.8305 - val_recall: 0.6049 - val_auc: 0.9131 - val_prc: 0.7129
Epoch 3/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0058 - tp: 163.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 151.0000 - accuracy: 0.9990 - precision: 0.8534 - recall: 0.5191 - auc: 0.9057 - prc: 0.6172 - val_loss: 0.0045 - val_tp: 50.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 31.0000 - val_accuracy: 0.9991 - val_precision: 0.8333 - val_recall: 0.6173 - val_auc: 0.9132 - val_prc: 0.7091
Epoch 4/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0053 - tp: 166.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 148.0000 - accuracy: 0.9990 - precision: 0.8426 - recall: 0.5287 - auc: 0.9187 - prc: 0.6479 - val_loss: 0.0043 - val_tp: 54.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 27.0000 - val_accuracy: 0.9992 - val_precision: 0.8438 - val_recall: 0.6667 - val_auc: 0.9195 - val_prc: 0.7355
Epoch 5/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0048 - tp: 177.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 137.0000 - accuracy: 0.9991 - precision: 0.8634 - recall: 0.5637 - auc: 0.9230 - prc: 0.7090 - val_loss: 0.0042 - val_tp: 56.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 25.0000 - val_accuracy: 0.9992 - val_precision: 0.8358 - val_recall: 0.6914 - val_auc: 0.9256 - val_prc: 0.7012
Epoch 6/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0049 - tp: 186.0000 - fp: 33.0000 - tn: 181929.0000 - fn: 128.0000 - accuracy: 0.9991 - precision: 0.8493 - recall: 0.5924 - auc: 0.9187 - prc: 0.6840 - val_loss: 0.0040 - val_tp: 55.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 26.0000 - val_accuracy: 0.9992 - val_precision: 0.8333 - val_recall: 0.6790 - val_auc: 0.9257 - val_prc: 0.7520
Epoch 7/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0043 - tp: 186.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 128.0000 - accuracy: 0.9992 - precision: 0.8774 - recall: 0.5924 - auc: 0.9222 - prc: 0.7255 - val_loss: 0.0040 - val_tp: 58.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8406 - val_recall: 0.7160 - val_auc: 0.9257 - val_prc: 0.7251
Epoch 8/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0044 - tp: 195.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 119.0000 - accuracy: 0.9992 - precision: 0.8864 - recall: 0.6210 - auc: 0.9143 - prc: 0.7114 - val_loss: 0.0038 - val_tp: 56.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 25.0000 - val_accuracy: 0.9992 - val_precision: 0.8358 - val_recall: 0.6914 - val_auc: 0.9195 - val_prc: 0.7571
Epoch 9/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0043 - tp: 198.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 116.0000 - accuracy: 0.9992 - precision: 0.8646 - recall: 0.6306 - auc: 0.9209 - prc: 0.7156 - val_loss: 0.0037 - val_tp: 55.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 26.0000 - val_accuracy: 0.9992 - val_precision: 0.8333 - val_recall: 0.6790 - val_auc: 0.9195 - val_prc: 0.7596
Epoch 10/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0042 - tp: 189.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 125.0000 - accuracy: 0.9992 - precision: 0.8873 - recall: 0.6019 - auc: 0.9209 - prc: 0.7199 - val_loss: 0.0037 - val_tp: 61.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8472 - val_recall: 0.7531 - val_auc: 0.9257 - val_prc: 0.7715
Epoch 11/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0043 - tp: 199.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8924 - recall: 0.6338 - auc: 0.9112 - prc: 0.6912 - val_loss: 0.0036 - val_tp: 59.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 22.0000 - val_accuracy: 0.9993 - val_precision: 0.8429 - val_recall: 0.7284 - val_auc: 0.9257 - val_prc: 0.7707
Epoch 12/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0042 - tp: 201.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8739 - recall: 0.6401 - auc: 0.9177 - prc: 0.7129 - val_loss: 0.0035 - val_tp: 55.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 26.0000 - val_accuracy: 0.9992 - val_precision: 0.8333 - val_recall: 0.6790 - val_auc: 0.9257 - val_prc: 0.7750
Epoch 13/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0040 - tp: 189.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 125.0000 - accuracy: 0.9992 - precision: 0.8791 - recall: 0.6019 - auc: 0.9258 - prc: 0.7330 - val_loss: 0.0035 - val_tp: 59.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 22.0000 - val_accuracy: 0.9993 - val_precision: 0.8429 - val_recall: 0.7284 - val_auc: 0.9257 - val_prc: 0.7765
Epoch 14/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0038 - tp: 206.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 108.0000 - accuracy: 0.9992 - precision: 0.8692 - recall: 0.6561 - auc: 0.9337 - prc: 0.7437 - val_loss: 0.0035 - val_tp: 59.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 22.0000 - val_accuracy: 0.9993 - val_precision: 0.8429 - val_recall: 0.7284 - val_auc: 0.9257 - val_prc: 0.7786
Epoch 15/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0040 - tp: 189.0000 - fp: 34.0000 - tn: 181928.0000 - fn: 125.0000 - accuracy: 0.9991 - precision: 0.8475 - recall: 0.6019 - auc: 0.9290 - prc: 0.7396 - val_loss: 0.0034 - val_tp: 60.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 21.0000 - val_accuracy: 0.9993 - val_precision: 0.8451 - val_recall: 0.7407 - val_auc: 0.9257 - val_prc: 0.7819
Epoch 16/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0037 - tp: 202.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 112.0000 - accuracy: 0.9992 - precision: 0.8783 - recall: 0.6433 - auc: 0.9306 - prc: 0.7534 - val_loss: 0.0034 - val_tp: 61.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8472 - val_recall: 0.7531 - val_auc: 0.9256 - val_prc: 0.7810
Epoch 17/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0038 - tp: 194.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 120.0000 - accuracy: 0.9992 - precision: 0.8858 - recall: 0.6178 - auc: 0.9306 - prc: 0.7401 - val_loss: 0.0034 - val_tp: 61.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8356 - val_recall: 0.7531 - val_auc: 0.9256 - val_prc: 0.7791
Epoch 18/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0040 - tp: 194.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 120.0000 - accuracy: 0.9992 - precision: 0.8778 - recall: 0.6178 - auc: 0.9274 - prc: 0.7235 - val_loss: 0.0034 - val_tp: 62.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 19.0000 - val_accuracy: 0.9993 - val_precision: 0.8378 - val_recall: 0.7654 - val_auc: 0.9256 - val_prc: 0.7815
Epoch 19/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0037 - tp: 204.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 110.0000 - accuracy: 0.9992 - precision: 0.8831 - recall: 0.6497 - auc: 0.9307 - prc: 0.7663 - val_loss: 0.0035 - val_tp: 63.0000 - val_fp: 13.0000 - val_tn: 45475.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8289 - val_recall: 0.7778 - val_auc: 0.9318 - val_prc: 0.7866
Epoch 20/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0038 - tp: 205.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 109.0000 - accuracy: 0.9993 - precision: 0.8874 - recall: 0.6529 - auc: 0.9306 - prc: 0.7374 - val_loss: 0.0035 - val_tp: 63.0000 - val_fp: 13.0000 - val_tn: 45475.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8289 - val_recall: 0.7778 - val_auc: 0.9318 - val_prc: 0.7875
Epoch 21/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 212.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8908 - recall: 0.6752 - auc: 0.9403 - prc: 0.7796 - val_loss: 0.0035 - val_tp: 63.0000 - val_fp: 13.0000 - val_tn: 45475.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8289 - val_recall: 0.7778 - val_auc: 0.9318 - val_prc: 0.7907
Epoch 22/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0037 - tp: 213.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8802 - recall: 0.6783 - auc: 0.9242 - prc: 0.7389 - val_loss: 0.0033 - val_tp: 61.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8472 - val_recall: 0.7531 - val_auc: 0.9318 - val_prc: 0.7946
Epoch 23/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0038 - tp: 198.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 116.0000 - accuracy: 0.9992 - precision: 0.8761 - recall: 0.6306 - auc: 0.9339 - prc: 0.7417 - val_loss: 0.0033 - val_tp: 61.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8472 - val_recall: 0.7531 - val_auc: 0.9318 - val_prc: 0.7950
Epoch 24/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0037 - tp: 199.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8884 - recall: 0.6338 - auc: 0.9275 - prc: 0.7536 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9318 - val_prc: 0.7971
Epoch 25/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0036 - tp: 208.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8851 - recall: 0.6624 - auc: 0.9403 - prc: 0.7603 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8514 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8047
Epoch 26/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 212.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8908 - recall: 0.6752 - auc: 0.9276 - prc: 0.7635 - val_loss: 0.0033 - val_tp: 62.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 19.0000 - val_accuracy: 0.9993 - val_precision: 0.8378 - val_recall: 0.7654 - val_auc: 0.9318 - val_prc: 0.7995
Epoch 27/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0036 - tp: 206.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 108.0000 - accuracy: 0.9993 - precision: 0.8918 - recall: 0.6561 - auc: 0.9340 - prc: 0.7629 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8007
Epoch 28/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0038 - tp: 217.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 97.0000 - accuracy: 0.9993 - precision: 0.8821 - recall: 0.6911 - auc: 0.9291 - prc: 0.7392 - val_loss: 0.0035 - val_tp: 63.0000 - val_fp: 13.0000 - val_tn: 45475.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8289 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.7940
Epoch 29/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 216.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 98.0000 - accuracy: 0.9993 - precision: 0.8780 - recall: 0.6879 - auc: 0.9292 - prc: 0.7584 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8047
Epoch 30/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0036 - tp: 215.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.8811 - recall: 0.6847 - auc: 0.9338 - prc: 0.7556 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8025
Epoch 31/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0037 - tp: 206.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 108.0000 - accuracy: 0.9993 - precision: 0.8803 - recall: 0.6561 - auc: 0.9339 - prc: 0.7494 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8059
Epoch 32/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0038 - tp: 201.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8894 - recall: 0.6401 - auc: 0.9308 - prc: 0.7472 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8043
Epoch 33/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 217.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 97.0000 - accuracy: 0.9993 - precision: 0.8857 - recall: 0.6911 - auc: 0.9355 - prc: 0.7679 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8051
Epoch 34/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0037 - tp: 209.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8782 - recall: 0.6656 - auc: 0.9355 - prc: 0.7411 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8046
Epoch 35/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 203.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8826 - recall: 0.6465 - auc: 0.9308 - prc: 0.7662 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8065
Epoch 36/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0036 - tp: 208.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8927 - recall: 0.6624 - auc: 0.9371 - prc: 0.7473 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 13.0000 - val_tn: 45475.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8289 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8080
Epoch 37/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 224.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 90.0000 - accuracy: 0.9993 - precision: 0.8854 - recall: 0.7134 - auc: 0.9324 - prc: 0.7676 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8081
Epoch 38/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0036 - tp: 210.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8714 - recall: 0.6688 - auc: 0.9308 - prc: 0.7517 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8035
Epoch 39/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0035 - tp: 213.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8838 - recall: 0.6783 - auc: 0.9340 - prc: 0.7633 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8132
Epoch 40/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0035 - tp: 206.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 108.0000 - accuracy: 0.9993 - precision: 0.8841 - recall: 0.6561 - auc: 0.9356 - prc: 0.7639 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8108
Epoch 41/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 211.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8828 - recall: 0.6720 - auc: 0.9388 - prc: 0.7732 - val_loss: 0.0034 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8123
Epoch 42/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 215.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.8884 - recall: 0.6847 - auc: 0.9356 - prc: 0.7786 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9442 - val_prc: 0.8159
Epoch 43/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 211.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8755 - recall: 0.6720 - auc: 0.9324 - prc: 0.7492 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9380 - val_prc: 0.8079
Epoch 44/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 203.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8865 - recall: 0.6465 - auc: 0.9324 - prc: 0.7567 - val_loss: 0.0033 - val_tp: 62.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8732 - val_recall: 0.7654 - val_auc: 0.9441 - val_prc: 0.8162
Epoch 45/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0035 - tp: 207.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 107.0000 - accuracy: 0.9993 - precision: 0.8809 - recall: 0.6592 - auc: 0.9355 - prc: 0.7558 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8229
Epoch 46/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0033 - tp: 216.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 98.0000 - accuracy: 0.9993 - precision: 0.8963 - recall: 0.6879 - auc: 0.9404 - prc: 0.7758 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8630 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8253
Epoch 47/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 212.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8760 - recall: 0.6752 - auc: 0.9371 - prc: 0.7657 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8514 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8245
Epoch 48/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 205.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8686 - recall: 0.6529 - auc: 0.9341 - prc: 0.7665 - val_loss: 0.0032 - val_tp: 62.0000 - val_fp: 7.0000 - val_tn: 45481.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8986 - val_recall: 0.7654 - val_auc: 0.9441 - val_prc: 0.8210
Epoch 49/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0034 - tp: 208.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8776 - recall: 0.6624 - auc: 0.9356 - prc: 0.7684 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8630 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8242
Epoch 50/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 211.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8903 - recall: 0.6720 - auc: 0.9340 - prc: 0.7772 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8195
Epoch 51/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 215.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.8884 - recall: 0.6847 - auc: 0.9420 - prc: 0.7773 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8630 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8200
Epoch 52/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 199.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8767 - recall: 0.6338 - auc: 0.9276 - prc: 0.7716 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8228
Epoch 53/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 203.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8865 - recall: 0.6465 - auc: 0.9483 - prc: 0.7781 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8212
Epoch 54/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0035 - tp: 206.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 108.0000 - accuracy: 0.9992 - precision: 0.8766 - recall: 0.6561 - auc: 0.9324 - prc: 0.7506 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8237
Epoch 55/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 209.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8894 - recall: 0.6656 - auc: 0.9325 - prc: 0.7780 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8630 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8266
Epoch 56/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 203.0000 - fp: 23.0000 - tn: 181939.0000 - fn: 111.0000 - accuracy: 0.9993 - precision: 0.8982 - recall: 0.6465 - auc: 0.9451 - prc: 0.7801 - val_loss: 0.0033 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9502 - val_prc: 0.8269
Epoch 57/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 208.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8739 - recall: 0.6624 - auc: 0.9435 - prc: 0.7781 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8274
Epoch 58/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 218.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 96.0000 - accuracy: 0.9993 - precision: 0.9008 - recall: 0.6943 - auc: 0.9388 - prc: 0.7856 - val_loss: 0.0032 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9441 - val_prc: 0.8222
Epoch 59/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 209.0000 - fp: 21.0000 - tn: 181941.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.9087 - recall: 0.6656 - auc: 0.9404 - prc: 0.7805 - val_loss: 0.0033 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9441 - val_prc: 0.8233
Epoch 60/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0032 - tp: 208.0000 - fp: 23.0000 - tn: 181939.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.9004 - recall: 0.6624 - auc: 0.9340 - prc: 0.7812 - val_loss: 0.0033 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9503 - val_prc: 0.8245
Epoch 61/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0030 - tp: 220.0000 - fp: 29.0000 - tn: 181933.0000 - fn: 94.0000 - accuracy: 0.9993 - precision: 0.8835 - recall: 0.7006 - auc: 0.9404 - prc: 0.7940 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8243
Epoch 62/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0032 - tp: 223.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 91.0000 - accuracy: 0.9994 - precision: 0.8956 - recall: 0.7102 - auc: 0.9356 - prc: 0.7857 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8514 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8238
Epoch 63/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0034 - tp: 206.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 108.0000 - accuracy: 0.9992 - precision: 0.8729 - recall: 0.6561 - auc: 0.9435 - prc: 0.7633 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8242
Epoch 64/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0031 - tp: 222.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 92.0000 - accuracy: 0.9994 - precision: 0.9024 - recall: 0.7070 - auc: 0.9356 - prc: 0.7868 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8514 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8318
Epoch 65/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0031 - tp: 213.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8875 - recall: 0.6783 - auc: 0.9373 - prc: 0.7931 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 7.0000 - val_tn: 45481.0000 - val_fn: 18.0000 - val_accuracy: 0.9995 - val_precision: 0.9000 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8334
Epoch 66/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 213.0000 - fp: 20.0000 - tn: 181942.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.9142 - recall: 0.6783 - auc: 0.9419 - prc: 0.7828 - val_loss: 0.0032 - val_tp: 64.0000 - val_fp: 10.0000 - val_tn: 45478.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8649 - val_recall: 0.7901 - val_auc: 0.9503 - val_prc: 0.8326
Epoch 67/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0031 - tp: 215.0000 - fp: 21.0000 - tn: 181941.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.9110 - recall: 0.6847 - auc: 0.9436 - prc: 0.7967 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9441 - val_prc: 0.8281
Epoch 68/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 212.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8870 - recall: 0.6752 - auc: 0.9452 - prc: 0.7885 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8329
Epoch 69/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0033 - tp: 209.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8819 - recall: 0.6656 - auc: 0.9371 - prc: 0.7721 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8345
Epoch 70/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0034 - tp: 209.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8708 - recall: 0.6656 - auc: 0.9403 - prc: 0.7689 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8338
Epoch 71/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0030 - tp: 223.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 91.0000 - accuracy: 0.9994 - precision: 0.8920 - recall: 0.7102 - auc: 0.9436 - prc: 0.7955 - val_loss: 0.0032 - val_tp: 58.0000 - val_fp: 7.0000 - val_tn: 45481.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8923 - val_recall: 0.7160 - val_auc: 0.9503 - val_prc: 0.8335
Epoch 72/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0033 - tp: 202.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 112.0000 - accuracy: 0.9993 - precision: 0.8938 - recall: 0.6433 - auc: 0.9339 - prc: 0.7595 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8332
Epoch 73/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 208.0000 - fp: 31.0000 - tn: 181931.0000 - fn: 106.0000 - accuracy: 0.9992 - precision: 0.8703 - recall: 0.6624 - auc: 0.9418 - prc: 0.7697 - val_loss: 0.0032 - val_tp: 58.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8788 - val_recall: 0.7160 - val_auc: 0.9503 - val_prc: 0.8364
Epoch 74/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 213.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8987 - recall: 0.6783 - auc: 0.9403 - prc: 0.7833 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8514 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8343
Epoch 75/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 210.0000 - fp: 19.0000 - tn: 181943.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.9170 - recall: 0.6688 - auc: 0.9388 - prc: 0.7823 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8339
Epoch 76/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 210.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8824 - recall: 0.6688 - auc: 0.9418 - prc: 0.7756 - val_loss: 0.0032 - val_tp: 58.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8788 - val_recall: 0.7160 - val_auc: 0.9503 - val_prc: 0.8351
Epoch 77/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0030 - tp: 214.0000 - fp: 23.0000 - tn: 181939.0000 - fn: 100.0000 - accuracy: 0.9993 - precision: 0.9030 - recall: 0.6815 - auc: 0.9420 - prc: 0.7937 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8341
Epoch 78/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 209.0000 - fp: 22.0000 - tn: 181940.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.9048 - recall: 0.6656 - auc: 0.9418 - prc: 0.7757 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8337
Epoch 79/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0032 - tp: 213.0000 - fp: 30.0000 - tn: 181932.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8765 - recall: 0.6783 - auc: 0.9403 - prc: 0.7737 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8873 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8342
Epoch 80/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0032 - tp: 212.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8833 - recall: 0.6752 - auc: 0.9403 - prc: 0.7720 - val_loss: 0.0032 - val_tp: 58.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8788 - val_recall: 0.7160 - val_auc: 0.9503 - val_prc: 0.8380
Epoch 81/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0031 - tp: 210.0000 - fp: 23.0000 - tn: 181939.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.9013 - recall: 0.6688 - auc: 0.9467 - prc: 0.8023 - val_loss: 0.0032 - val_tp: 64.0000 - val_fp: 11.0000 - val_tn: 45477.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8533 - val_recall: 0.7901 - val_auc: 0.9502 - val_prc: 0.8332
Epoch 82/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0030 - tp: 216.0000 - fp: 28.0000 - tn: 181934.0000 - fn: 98.0000 - accuracy: 0.9993 - precision: 0.8852 - recall: 0.6879 - auc: 0.9467 - prc: 0.8001 - val_loss: 0.0032 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9503 - val_prc: 0.8333
Epoch 83/100
90/90 [==============================] - 1s 6ms/step - loss: 0.0032 - tp: 214.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 100.0000 - accuracy: 0.9993 - precision: 0.8880 - recall: 0.6815 - auc: 0.9435 - prc: 0.7755 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8357
Epoch 84/100
90/90 [==============================] - 0s 6ms/step - loss: 0.0030 - tp: 216.0000 - fp: 21.0000 - tn: 181941.0000 - fn: 98.0000 - accuracy: 0.9993 - precision: 0.9114 - recall: 0.6879 - auc: 0.9451 - prc: 0.7989 - val_loss: 0.0032 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9503 - val_prc: 0.8344
Epoch 85/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 211.0000 - fp: 25.0000 - tn: 181937.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8941 - recall: 0.6720 - auc: 0.9403 - prc: 0.7796 - val_loss: 0.0032 - val_tp: 63.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8368
Epoch 86/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 206.0000 - fp: 27.0000 - tn: 181935.0000 - fn: 108.0000 - accuracy: 0.9993 - precision: 0.8841 - recall: 0.6561 - auc: 0.9515 - prc: 0.7932 - val_loss: 0.0033 - val_tp: 64.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8421 - val_recall: 0.7901 - val_auc: 0.9503 - val_prc: 0.8350
Epoch 87/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0033 - tp: 208.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8966 - recall: 0.6624 - auc: 0.9403 - prc: 0.7714 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 9.0000 - val_tn: 45479.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8372
Epoch 88/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0032 - tp: 215.0000 - fp: 26.0000 - tn: 181936.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.8921 - recall: 0.6847 - auc: 0.9482 - prc: 0.7848 - val_loss: 0.0033 - val_tp: 63.0000 - val_fp: 12.0000 - val_tn: 45476.0000 - val_fn: 18.0000 - val_accuracy: 0.9993 - val_precision: 0.8400 - val_recall: 0.7778 - val_auc: 0.9503 - val_prc: 0.8360
Epoch 89/100
90/90 [==============================] - 0s 5ms/step - loss: 0.0030 - tp: 224.0000 - fp: 24.0000 - tn: 181938.0000 - fn: 90.0000 - accuracy: 0.9994 - precision: 0.9032 - recall: 0.7134 - auc: 0.9451 - prc: 0.7970 - val_loss: 0.0032 - val_tp: 58.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 23.0000 - val_accuracy: 0.9993 - val_precision: 0.8788 - val_recall: 0.7160 - val_auc: 0.9503 - val_prc: 0.8369
Epoch 90/100
79/90 [=========================>....] - ETA: 0s - loss: 0.0033 - tp: 186.0000 - fp: 20.0000 - tn: 161496.0000 - fn: 90.0000 - accuracy: 0.9993 - precision: 0.9029 - recall: 0.6739 - auc: 0.9448 - prc: 0.7648Restoring model weights from the end of the best epoch: 80.
90/90 [==============================] - 0s 6ms/step - loss: 0.0031 - tp: 218.0000 - fp: 22.0000 - tn: 181940.0000 - fn: 96.0000 - accuracy: 0.9994 - precision: 0.9083 - recall: 0.6943 - auc: 0.9467 - prc: 0.7786 - val_loss: 0.0032 - val_tp: 60.0000 - val_fp: 8.0000 - val_tn: 45480.0000 - val_fn: 21.0000 - val_accuracy: 0.9994 - val_precision: 0.8824 - val_recall: 0.7407 - val_auc: 0.9503 - val_prc: 0.8375
Epoch 90: early stopping

Check training history

In this section, you will produce plots of your model's accuracy and loss on the training and validation set. These are useful to check for overfitting, which you can learn more about in the Overfit and underfit tutorial.

Additionally, you can produce these plots for any of the metrics you created above. False negatives are included as an example.

def plot_metrics(history):
  metrics = ['loss', 'prc', 'precision', 'recall']
  for n, metric in enumerate(metrics):
    name = metric.replace("_"," ").capitalize()
    plt.subplot(2,2,n+1)
    plt.plot(history.epoch, history.history[metric], color=colors[0], label='Train')
    plt.plot(history.epoch, history.history['val_'+metric],
             color=colors[0], linestyle="--", label='Val')
    plt.xlabel('Epoch')
    plt.ylabel(name)
    if metric == 'loss':
      plt.ylim([0, plt.ylim()[1]])
    elif metric == 'auc':
      plt.ylim([0.8,1])
    else:
      plt.ylim([0,1])

    plt.legend()

plot_metrics(baseline_history)

Note: That the validation curve generally performs better than the training curve. This is mainly caused by the fact that the dropout layer is not active when evaluating the model.

Evaluate metrics

You can use a confusion matrix to summarize the actual vs. predicted labels, where the X axis is the predicted label and the Y axis is the actual label:

train_predictions_baseline = model.predict(train_features, batch_size=BATCH_SIZE)
test_predictions_baseline = model.predict(test_features, batch_size=BATCH_SIZE)

90/90 [==============================] - 0s 1ms/step
28/28 [==============================] - 0s 1ms/step

def plot_cm(labels, predictions, p=0.5):
  cm = confusion_matrix(labels, predictions > p)
  plt.figure(figsize=(5,5))
  sns.heatmap(cm, annot=True, fmt="d")
  plt.title('Confusion matrix @{:.2f}'.format(p))
  plt.ylabel('Actual label')
  plt.xlabel('Predicted label')

  print('Legitimate Transactions Detected (True Negatives): ', cm[0][0])
  print('Legitimate Transactions Incorrectly Detected (False Positives): ', cm[0][1])
  print('Fraudulent Transactions Missed (False Negatives): ', cm[1][0])
  print('Fraudulent Transactions Detected (True Positives): ', cm[1][1])
  print('Total Fraudulent Transactions: ', np.sum(cm[1]))

Evaluate your model on the test dataset and display the results for the metrics you created above:

baseline_results = model.evaluate(test_features, test_labels,
                                  batch_size=BATCH_SIZE, verbose=0)
for name, value in zip(model.metrics_names, baseline_results):
  print(name, ': ', value)
print()

plot_cm(test_labels, test_predictions_baseline)

loss :  0.0034967793617397547
tp :  72.0
fp :  8.0
tn :  56857.0
fn :  25.0
accuracy :  0.9994206428527832
precision :  0.8999999761581421
recall :  0.7422680258750916
auc :  0.927476704120636
prc :  0.7999517917633057

Legitimate Transactions Detected (True Negatives):  56857
Legitimate Transactions Incorrectly Detected (False Positives):  8
Fraudulent Transactions Missed (False Negatives):  25
Fraudulent Transactions Detected (True Positives):  72
Total Fraudulent Transactions:  97

If the model had predicted everything perfectly, this would be a diagonal matrix where values off the main diagonal, indicating incorrect predictions, would be zero. In this case the matrix shows that you have relatively few false positives, meaning that there were relatively few legitimate transactions that were incorrectly flagged. However, you would likely want to have even fewer false negatives despite the cost of increasing the number of false positives. This trade off may be preferable because false negatives would allow fraudulent transactions to go through, whereas false positives may cause an email to be sent to a customer to ask them to verify their card activity.

Plot the ROC

Now plot the ROC. This plot is useful because it shows, at a glance, the range of performance the model can reach just by tuning the output threshold.

def plot_roc(name, labels, predictions, **kwargs):
  fp, tp, _ = sklearn.metrics.roc_curve(labels, predictions)

  plt.plot(100*fp, 100*tp, label=name, linewidth=2, **kwargs)
  plt.xlabel('False positives [%]')
  plt.ylabel('True positives [%]')
  plt.xlim([-0.5,20])
  plt.ylim([80,100.5])
  plt.grid(True)
  ax = plt.gca()
  ax.set_aspect('equal')

plot_roc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_roc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')
plt.legend(loc='lower right');

Plot the AUPRC

Now plot the AUPRC. Area under the interpolated precision-recall curve, obtained by plotting (recall, precision) points for different values of the classification threshold. Depending on how it's calculated, PR AUC may be equivalent to the average precision of the model.

def plot_prc(name, labels, predictions, **kwargs):
    precision, recall, _ = sklearn.metrics.precision_recall_curve(labels, predictions)

    plt.plot(precision, recall, label=name, linewidth=2, **kwargs)
    plt.xlabel('Precision')
    plt.ylabel('Recall')
    plt.grid(True)
    ax = plt.gca()
    ax.set_aspect('equal')

plot_prc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_prc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')
plt.legend(loc='lower right');

It looks like the precision is relatively high, but the recall and the area under the ROC curve (AUC) aren't as high as you might like. Classifiers often face challenges when trying to maximize both precision and recall, which is especially true when working with imbalanced datasets. It is important to consider the costs of different types of errors in the context of the problem you care about. In this example, a false negative (a fraudulent transaction is missed) may have a financial cost, while a false positive (a transaction is incorrectly flagged as fraudulent) may decrease user happiness.

Class weights

Calculate class weights

The goal is to identify fraudulent transactions, but you don't have very many of those positive samples to work with, so you would want to have the classifier heavily weight the few examples that are available. You can do this by passing Keras weights for each class through a parameter. These will cause the model to "pay more attention" to examples from an under-represented class.

# Scaling by total/2 helps keep the loss to a similar magnitude.
# The sum of the weights of all examples stays the same.
weight_for_0 = (1 / neg) * (total / 2.0)
weight_for_1 = (1 / pos) * (total / 2.0)

class_weight = {0: weight_for_0, 1: weight_for_1}

print('Weight for class 0: {:.2f}'.format(weight_for_0))
print('Weight for class 1: {:.2f}'.format(weight_for_1))

Weight for class 0: 0.50
Weight for class 1: 289.44

Train a model with class weights

Now try re-training and evaluating the model with class weights to see how that affects the predictions.

Note: Using class_weights changes the range of the loss. This may affect the stability of the training depending on the optimizer. Optimizers whose step size is dependent on the magnitude of the gradient, like tf.keras.optimizers.SGD, may fail. The optimizer used here, tf.keras.optimizers.Adam, is unaffected by the scaling change. Also note that because of the weighting, the total losses are not comparable between the two models.

weighted_model = make_model()
weighted_model.load_weights(initial_weights)

weighted_history = weighted_model.fit(
    train_features,
    train_labels,
    batch_size=BATCH_SIZE,
    epochs=EPOCHS,
    callbacks=[early_stopping],
    validation_data=(val_features, val_labels),
    # The class weights go here
    class_weight=class_weight)

Epoch 1/100
90/90 [==============================] - 2s 11ms/step - loss: 1.1025 - tp: 210.0000 - fp: 588.0000 - tn: 238239.0000 - fn: 201.0000 - accuracy: 0.9967 - precision: 0.2632 - recall: 0.5109 - auc: 0.8965 - prc: 0.3408 - val_loss: 0.0114 - val_tp: 56.0000 - val_fp: 41.0000 - val_tn: 45447.0000 - val_fn: 25.0000 - val_accuracy: 0.9986 - val_precision: 0.5773 - val_recall: 0.6914 - val_auc: 0.9455 - val_prc: 0.6191
Epoch 2/100
90/90 [==============================] - 1s 6ms/step - loss: 0.5621 - tp: 223.0000 - fp: 1125.0000 - tn: 180837.0000 - fn: 91.0000 - accuracy: 0.9933 - precision: 0.1654 - recall: 0.7102 - auc: 0.9329 - prc: 0.4102 - val_loss: 0.0168 - val_tp: 67.0000 - val_fp: 81.0000 - val_tn: 45407.0000 - val_fn: 14.0000 - val_accuracy: 0.9979 - val_precision: 0.4527 - val_recall: 0.8272 - val_auc: 0.9617 - val_prc: 0.6582
Epoch 3/100
90/90 [==============================] - 1s 6ms/step - loss: 0.4982 - tp: 229.0000 - fp: 1838.0000 - tn: 180124.0000 - fn: 85.0000 - accuracy: 0.9895 - precision: 0.1108 - recall: 0.7293 - auc: 0.9385 - prc: 0.3783 - val_loss: 0.0244 - val_tp: 67.0000 - val_fp: 145.0000 - val_tn: 45343.0000 - val_fn: 14.0000 - val_accuracy: 0.9965 - val_precision: 0.3160 - val_recall: 0.8272 - val_auc: 0.9612 - val_prc: 0.6633
Epoch 4/100
90/90 [==============================] - 0s 6ms/step - loss: 0.3663 - tp: 246.0000 - fp: 3063.0000 - tn: 178899.0000 - fn: 68.0000 - accuracy: 0.9828 - precision: 0.0743 - recall: 0.7834 - auc: 0.9502 - prc: 0.3940 - val_loss: 0.0333 - val_tp: 67.0000 - val_fp: 221.0000 - val_tn: 45267.0000 - val_fn: 14.0000 - val_accuracy: 0.9948 - val_precision: 0.2326 - val_recall: 0.8272 - val_auc: 0.9658 - val_prc: 0.6699
Epoch 5/100
90/90 [==============================] - 1s 6ms/step - loss: 0.3579 - tp: 251.0000 - fp: 4357.0000 - tn: 177605.0000 - fn: 63.0000 - accuracy: 0.9758 - precision: 0.0545 - recall: 0.7994 - auc: 0.9478 - prc: 0.3349 - val_loss: 0.0446 - val_tp: 70.0000 - val_fp: 354.0000 - val_tn: 45134.0000 - val_fn: 11.0000 - val_accuracy: 0.9920 - val_precision: 0.1651 - val_recall: 0.8642 - val_auc: 0.9685 - val_prc: 0.6304
Epoch 6/100
90/90 [==============================] - 1s 6ms/step - loss: 0.3682 - tp: 259.0000 - fp: 5524.0000 - tn: 176438.0000 - fn: 55.0000 - accuracy: 0.9694 - precision: 0.0448 - recall: 0.8248 - auc: 0.9403 - prc: 0.2853 - val_loss: 0.0539 - val_tp: 71.0000 - val_fp: 515.0000 - val_tn: 44973.0000 - val_fn: 10.0000 - val_accuracy: 0.9885 - val_precision: 0.1212 - val_recall: 0.8765 - val_auc: 0.9691 - val_prc: 0.5536
Epoch 7/100
90/90 [==============================] - 1s 6ms/step - loss: 0.2656 - tp: 272.0000 - fp: 6172.0000 - tn: 175790.0000 - fn: 42.0000 - accuracy: 0.9659 - precision: 0.0422 - recall: 0.8662 - auc: 0.9638 - prc: 0.2857 - val_loss: 0.0598 - val_tp: 72.0000 - val_fp: 610.0000 - val_tn: 44878.0000 - val_fn: 9.0000 - val_accuracy: 0.9864 - val_precision: 0.1056 - val_recall: 0.8889 - val_auc: 0.9684 - val_prc: 0.5479
Epoch 8/100
90/90 [==============================] - 0s 6ms/step - loss: 0.2976 - tp: 269.0000 - fp: 6541.0000 - tn: 175421.0000 - fn: 45.0000 - accuracy: 0.9639 - precision: 0.0395 - recall: 0.8567 - auc: 0.9509 - prc: 0.2741 - val_loss: 0.0647 - val_tp: 72.0000 - val_fp: 665.0000 - val_tn: 44823.0000 - val_fn: 9.0000 - val_accuracy: 0.9852 - val_precision: 0.0977 - val_recall: 0.8889 - val_auc: 0.9680 - val_prc: 0.5290
Epoch 9/100
90/90 [==============================] - 0s 6ms/step - loss: 0.2602 - tp: 271.0000 - fp: 7145.0000 - tn: 174817.0000 - fn: 43.0000 - accuracy: 0.9606 - precision: 0.0365 - recall: 0.8631 - auc: 0.9636 - prc: 0.2577 - val_loss: 0.0696 - val_tp: 73.0000 - val_fp: 733.0000 - val_tn: 44755.0000 - val_fn: 8.0000 - val_accuracy: 0.9837 - val_precision: 0.0906 - val_recall: 0.9012 - val_auc: 0.9684 - val_prc: 0.5221
Epoch 10/100
90/90 [==============================] - 1s 6ms/step - loss: 0.2536 - tp: 276.0000 - fp: 7339.0000 - tn: 174623.0000 - fn: 38.0000 - accuracy: 0.9595 - precision: 0.0362 - recall: 0.8790 - auc: 0.9638 - prc: 0.2559 - val_loss: 0.0731 - val_tp: 73.0000 - val_fp: 782.0000 - val_tn: 44706.0000 - val_fn: 8.0000 - val_accuracy: 0.9827 - val_precision: 0.0854 - val_recall: 0.9012 - val_auc: 0.9684 - val_prc: 0.5147
Epoch 11/100
90/90 [==============================] - 1s 6ms/step - loss: 0.2511 - tp: 272.0000 - fp: 7558.0000 - tn: 174404.0000 - fn: 42.0000 - accuracy: 0.9583 - precision: 0.0347 - recall: 0.8662 - auc: 0.9650 - prc: 0.2357 - val_loss: 0.0782 - val_tp: 74.0000 - val_fp: 861.0000 - val_tn: 44627.0000 - val_fn: 7.0000 - val_accuracy: 0.9810 - val_precision: 0.0791 - val_recall: 0.9136 - val_auc: 0.9688 - val_prc: 0.4952
Epoch 12/100
90/90 [==============================] - 1s 6ms/step - loss: 0.2387 - tp: 278.0000 - fp: 7560.0000 - tn: 174402.0000 - fn: 36.0000 - accuracy: 0.9583 - precision: 0.0355 - recall: 0.8854 - auc: 0.9701 - prc: 0.2369 - val_loss: 0.0789 - val_tp: 74.0000 - val_fp: 872.0000 - val_tn: 44616.0000 - val_fn: 7.0000 - val_accuracy: 0.9807 - val_precision: 0.0782 - val_recall: 0.9136 - val_auc: 0.9708 - val_prc: 0.5010
Epoch 13/100
90/90 [==============================] - 1s 6ms/step - loss: 0.2682 - tp: 278.0000 - fp: 7623.0000 - tn: 174339.0000 - fn: 36.0000 - accuracy: 0.9580 - precision: 0.0352 - recall: 0.8854 - auc: 0.9593 - prc: 0.2581 - val_loss: 0.0774 - val_tp: 74.0000 - val_fp: 849.0000 - val_tn: 44639.0000 - val_fn: 7.0000 - val_accuracy: 0.9812 - val_precision: 0.0802 - val_recall: 0.9136 - val_auc: 0.9712 - val_prc: 0.5023
Epoch 14/100
86/90 [===========================>..] - ETA: 0s - loss: 0.2844 - tp: 267.0000 - fp: 7282.0000 - tn: 168541.0000 - fn: 38.0000 - accuracy: 0.9584 - precision: 0.0354 - recall: 0.8754 - auc: 0.9561 - prc: 0.2436Restoring model weights from the end of the best epoch: 4.
90/90 [==============================] - 1s 6ms/step - loss: 0.2914 - tp: 273.0000 - fp: 7515.0000 - tn: 174447.0000 - fn: 41.0000 - accuracy: 0.9585 - precision: 0.0351 - recall: 0.8694 - auc: 0.9550 - prc: 0.2436 - val_loss: 0.0797 - val_tp: 75.0000 - val_fp: 882.0000 - val_tn: 44606.0000 - val_fn: 6.0000 - val_accuracy: 0.9805 - val_precision: 0.0784 - val_recall: 0.9259 - val_auc: 0.9708 - val_prc: 0.5038
Epoch 14: early stopping

Check training history

plot_metrics(weighted_history)

Evaluate metrics

train_predictions_weighted = weighted_model.predict(train_features, batch_size=BATCH_SIZE)
test_predictions_weighted = weighted_model.predict(test_features, batch_size=BATCH_SIZE)

90/90 [==============================] - 0s 1ms/step
28/28 [==============================] - 0s 1ms/step

weighted_results = weighted_model.evaluate(test_features, test_labels,
                                           batch_size=BATCH_SIZE, verbose=0)
for name, value in zip(weighted_model.metrics_names, weighted_results):
  print(name, ': ', value)
print()

plot_cm(test_labels, test_predictions_weighted)

loss :  0.03274456411600113
tp :  81.0
fp :  252.0
tn :  56613.0
fn :  16.0
accuracy :  0.9952951073646545
precision :  0.2432432472705841
recall :  0.8350515365600586
auc :  0.9679247140884399
prc :  0.6531848311424255

Legitimate Transactions Detected (True Negatives):  56613
Legitimate Transactions Incorrectly Detected (False Positives):  252
Fraudulent Transactions Missed (False Negatives):  16
Fraudulent Transactions Detected (True Positives):  81
Total Fraudulent Transactions:  97

Here you can see that with class weights the accuracy and precision are lower because there are more false positives, but conversely the recall and AUC are higher because the model also found more true positives. Despite having lower accuracy, this model has higher recall (and identifies more fraudulent transactions). Of course, there is a cost to both types of error (you wouldn't want to bug users by flagging too many legitimate transactions as fraudulent, either). Carefully consider the trade-offs between these different types of errors for your application.

Plot the ROC

plot_roc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_roc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')

plot_roc("Train Weighted", train_labels, train_predictions_weighted, color=colors[1])
plot_roc("Test Weighted", test_labels, test_predictions_weighted, color=colors[1], linestyle='--')


plt.legend(loc='lower right');

Plot the AUPRC

plot_prc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_prc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')

plot_prc("Train Weighted", train_labels, train_predictions_weighted, color=colors[1])
plot_prc("Test Weighted", test_labels, test_predictions_weighted, color=colors[1], linestyle='--')


plt.legend(loc='lower right');

Oversampling

Oversample the minority class

A related approach would be to resample the dataset by oversampling the minority class.

pos_features = train_features[bool_train_labels]
neg_features = train_features[~bool_train_labels]

pos_labels = train_labels[bool_train_labels]
neg_labels = train_labels[~bool_train_labels]

Using NumPy

You can balance the dataset manually by choosing the right number of random indices from the positive examples:

ids = np.arange(len(pos_features))
choices = np.random.choice(ids, len(neg_features))

res_pos_features = pos_features[choices]
res_pos_labels = pos_labels[choices]

res_pos_features.shape

(181962, 29)

resampled_features = np.concatenate([res_pos_features, neg_features], axis=0)
resampled_labels = np.concatenate([res_pos_labels, neg_labels], axis=0)

order = np.arange(len(resampled_labels))
np.random.shuffle(order)
resampled_features = resampled_features[order]
resampled_labels = resampled_labels[order]

resampled_features.shape

(363924, 29)

Using tf.data

If you're using tf.data the easiest way to produce balanced examples is to start with a positive and a negative dataset, and merge them. See the tf.data guide for more examples.

BUFFER_SIZE = 100000

def make_ds(features, labels):
  ds = tf.data.Dataset.from_tensor_slices((features, labels))#.cache()
  ds = ds.shuffle(BUFFER_SIZE).repeat()
  return ds

pos_ds = make_ds(pos_features, pos_labels)
neg_ds = make_ds(neg_features, neg_labels)

Each dataset provides (feature, label) pairs:

for features, label in pos_ds.take(1):
  print("Features:\n", features.numpy())
  print()
  print("Label: ", label.numpy())

Features:
 [-1.45352952  0.79696871 -0.66601721  1.19337228 -0.53348935 -0.59578957
 -2.0979605   0.8951992  -1.03275912 -3.61762633  2.51868193 -2.2973935
  0.56276617 -5.         -2.0200714  -2.99465523 -5.         -1.470018
  0.49047894  0.01528834  0.71729537  0.3147249  -1.19057248 -0.11189896
  0.41024869 -0.93852853  0.85165508  0.58924332 -0.06818104]

Label:  1

Merge the two together using tf.data.Dataset.sample_from_datasets:

resampled_ds = tf.data.Dataset.sample_from_datasets([pos_ds, neg_ds], weights=[0.5, 0.5])
resampled_ds = resampled_ds.batch(BATCH_SIZE).prefetch(2)

for features, label in resampled_ds.take(1):
  print(label.numpy().mean())

0.50927734375

To use this dataset, you'll need the number of steps per epoch.

The definition of "epoch" in this case is less clear. Say it's the number of batches required to see each negative example once:

resampled_steps_per_epoch = np.ceil(2.0*neg/BATCH_SIZE)
resampled_steps_per_epoch

278.0

Train on the oversampled data

Now try training the model with the resampled data set instead of using class weights to see how these methods compare.

Note: Because the data was balanced by replicating the positive examples, the total dataset size is larger, and each epoch runs for more training steps.

resampled_model = make_model()
resampled_model.load_weights(initial_weights)

# Reset the bias to zero, since this dataset is balanced.
output_layer = resampled_model.layers[-1] 
output_layer.bias.assign([0])

val_ds = tf.data.Dataset.from_tensor_slices((val_features, val_labels)).cache()
val_ds = val_ds.batch(BATCH_SIZE).prefetch(2) 

resampled_history = resampled_model.fit(
    resampled_ds,
    epochs=EPOCHS,
    steps_per_epoch=resampled_steps_per_epoch,
    callbacks=[early_stopping],
    validation_data=val_ds)

Epoch 1/100
278/278 [==============================] - 9s 26ms/step - loss: 0.3300 - tp: 261082.0000 - fp: 67295.0000 - tn: 274419.0000 - fn: 23510.0000 - accuracy: 0.8550 - precision: 0.7951 - recall: 0.9174 - auc: 0.9558 - prc: 0.9586 - val_loss: 0.1785 - val_tp: 75.0000 - val_fp: 1195.0000 - val_tn: 44293.0000 - val_fn: 6.0000 - val_accuracy: 0.9736 - val_precision: 0.0591 - val_recall: 0.9259 - val_auc: 0.9764 - val_prc: 0.7125
Epoch 2/100
278/278 [==============================] - 6s 23ms/step - loss: 0.1676 - tp: 264165.0000 - fp: 16889.0000 - tn: 267825.0000 - fn: 20465.0000 - accuracy: 0.9344 - precision: 0.9399 - recall: 0.9281 - auc: 0.9838 - prc: 0.9859 - val_loss: 0.0980 - val_tp: 75.0000 - val_fp: 974.0000 - val_tn: 44514.0000 - val_fn: 6.0000 - val_accuracy: 0.9785 - val_precision: 0.0715 - val_recall: 0.9259 - val_auc: 0.9755 - val_prc: 0.7231
Epoch 3/100
278/278 [==============================] - 6s 23ms/step - loss: 0.1284 - tp: 268163.0000 - fp: 12440.0000 - tn: 271299.0000 - fn: 17442.0000 - accuracy: 0.9475 - precision: 0.9557 - recall: 0.9389 - auc: 0.9910 - prc: 0.9916 - val_loss: 0.0751 - val_tp: 75.0000 - val_fp: 901.0000 - val_tn: 44587.0000 - val_fn: 6.0000 - val_accuracy: 0.9801 - val_precision: 0.0768 - val_recall: 0.9259 - val_auc: 0.9744 - val_prc: 0.7121
Epoch 4/100
278/278 [==============================] - 7s 24ms/step - loss: 0.1085 - tp: 270417.0000 - fp: 10773.0000 - tn: 273770.0000 - fn: 14384.0000 - accuracy: 0.9558 - precision: 0.9617 - recall: 0.9495 - auc: 0.9939 - prc: 0.9940 - val_loss: 0.0620 - val_tp: 75.0000 - val_fp: 851.0000 - val_tn: 44637.0000 - val_fn: 6.0000 - val_accuracy: 0.9812 - val_precision: 0.0810 - val_recall: 0.9259 - val_auc: 0.9754 - val_prc: 0.6973
Epoch 5/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0972 - tp: 272156.0000 - fp: 10008.0000 - tn: 274621.0000 - fn: 12559.0000 - accuracy: 0.9604 - precision: 0.9645 - recall: 0.9559 - auc: 0.9951 - prc: 0.9950 - val_loss: 0.0549 - val_tp: 75.0000 - val_fp: 842.0000 - val_tn: 44646.0000 - val_fn: 6.0000 - val_accuracy: 0.9814 - val_precision: 0.0818 - val_recall: 0.9259 - val_auc: 0.9692 - val_prc: 0.6978
Epoch 6/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0895 - tp: 273467.0000 - fp: 9649.0000 - tn: 275101.0000 - fn: 11127.0000 - accuracy: 0.9635 - precision: 0.9659 - recall: 0.9609 - auc: 0.9958 - prc: 0.9956 - val_loss: 0.0485 - val_tp: 75.0000 - val_fp: 782.0000 - val_tn: 44706.0000 - val_fn: 6.0000 - val_accuracy: 0.9827 - val_precision: 0.0875 - val_recall: 0.9259 - val_auc: 0.9667 - val_prc: 0.7006
Epoch 7/100
278/278 [==============================] - 7s 24ms/step - loss: 0.0832 - tp: 274498.0000 - fp: 9373.0000 - tn: 275563.0000 - fn: 9910.0000 - accuracy: 0.9661 - precision: 0.9670 - recall: 0.9652 - auc: 0.9963 - prc: 0.9962 - val_loss: 0.0451 - val_tp: 74.0000 - val_fp: 749.0000 - val_tn: 44739.0000 - val_fn: 7.0000 - val_accuracy: 0.9834 - val_precision: 0.0899 - val_recall: 0.9136 - val_auc: 0.9680 - val_prc: 0.6990
Epoch 8/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0788 - tp: 275682.0000 - fp: 9166.0000 - tn: 275405.0000 - fn: 9091.0000 - accuracy: 0.9679 - precision: 0.9678 - recall: 0.9681 - auc: 0.9966 - prc: 0.9964 - val_loss: 0.0422 - val_tp: 74.0000 - val_fp: 729.0000 - val_tn: 44759.0000 - val_fn: 7.0000 - val_accuracy: 0.9838 - val_precision: 0.0922 - val_recall: 0.9136 - val_auc: 0.9689 - val_prc: 0.7002
Epoch 9/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0747 - tp: 276283.0000 - fp: 8934.0000 - tn: 275833.0000 - fn: 8294.0000 - accuracy: 0.9697 - precision: 0.9687 - recall: 0.9709 - auc: 0.9969 - prc: 0.9967 - val_loss: 0.0399 - val_tp: 75.0000 - val_fp: 682.0000 - val_tn: 44806.0000 - val_fn: 6.0000 - val_accuracy: 0.9849 - val_precision: 0.0991 - val_recall: 0.9259 - val_auc: 0.9695 - val_prc: 0.7007
Epoch 10/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0720 - tp: 277998.0000 - fp: 8933.0000 - tn: 275246.0000 - fn: 7167.0000 - accuracy: 0.9717 - precision: 0.9689 - recall: 0.9749 - auc: 0.9971 - prc: 0.9968 - val_loss: 0.0383 - val_tp: 73.0000 - val_fp: 682.0000 - val_tn: 44806.0000 - val_fn: 8.0000 - val_accuracy: 0.9849 - val_precision: 0.0967 - val_recall: 0.9012 - val_auc: 0.9698 - val_prc: 0.7018
Epoch 11/100
278/278 [==============================] - 6s 23ms/step - loss: 0.0692 - tp: 278186.0000 - fp: 8659.0000 - tn: 276014.0000 - fn: 6485.0000 - accuracy: 0.9734 - precision: 0.9698 - recall: 0.9772 - auc: 0.9973 - prc: 0.9970 - val_loss: 0.0367 - val_tp: 74.0000 - val_fp: 660.0000 - val_tn: 44828.0000 - val_fn: 7.0000 - val_accuracy: 0.9854 - val_precision: 0.1008 - val_recall: 0.9136 - val_auc: 0.9702 - val_prc: 0.7020
Epoch 12/100
276/278 [============================>.] - ETA: 0s - loss: 0.0670 - tp: 276112.0000 - fp: 8604.0000 - tn: 274316.0000 - fn: 6216.0000 - accuracy: 0.9738 - precision: 0.9698 - recall: 0.9780 - auc: 0.9974 - prc: 0.9971Restoring model weights from the end of the best epoch: 2.
278/278 [==============================] - 6s 23ms/step - loss: 0.0671 - tp: 278092.0000 - fp: 8677.0000 - tn: 276316.0000 - fn: 6259.0000 - accuracy: 0.9738 - precision: 0.9697 - recall: 0.9780 - auc: 0.9974 - prc: 0.9971 - val_loss: 0.0353 - val_tp: 74.0000 - val_fp: 633.0000 - val_tn: 44855.0000 - val_fn: 7.0000 - val_accuracy: 0.9860 - val_precision: 0.1047 - val_recall: 0.9136 - val_auc: 0.9704 - val_prc: 0.7018
Epoch 12: early stopping

If the training process were considering the whole dataset on each gradient update, this oversampling would be basically identical to the class weighting.

But when training the model batch-wise, as you did here, the oversampled data provides a smoother gradient signal: Instead of each positive example being shown in one batch with a large weight, they're shown in many different batches each time with a small weight.

This smoother gradient signal makes it easier to train the model.

Check training history

Note that the distributions of metrics will be different here, because the training data has a totally different distribution from the validation and test data.

plot_metrics(resampled_history)

Re-train

Because training is easier on the balanced data, the above training procedure may overfit quickly.

So break up the epochs to give the tf.keras.callbacks.EarlyStopping finer control over when to stop training.

resampled_model = make_model()
resampled_model.load_weights(initial_weights)

# Reset the bias to zero, since this dataset is balanced.
output_layer = resampled_model.layers[-1] 
output_layer.bias.assign([0])

resampled_history = resampled_model.fit(
    resampled_ds,
    # These are not real epochs
    steps_per_epoch=20,
    epochs=10*EPOCHS,
    callbacks=[early_stopping],
    validation_data=(val_ds))

Epoch 1/1000
20/20 [==============================] - 3s 51ms/step - loss: 0.6201 - tp: 18361.0000 - fp: 12180.0000 - tn: 53666.0000 - fn: 2322.0000 - accuracy: 0.8324 - precision: 0.6012 - recall: 0.8877 - auc: 0.9476 - prc: 0.8715 - val_loss: 0.8273 - val_tp: 78.0000 - val_fp: 24283.0000 - val_tn: 21205.0000 - val_fn: 3.0000 - val_accuracy: 0.4670 - val_precision: 0.0032 - val_recall: 0.9630 - val_auc: 0.9378 - val_prc: 0.4261
Epoch 2/1000
20/20 [==============================] - 1s 27ms/step - loss: 0.5165 - tp: 18820.0000 - fp: 10072.0000 - tn: 10384.0000 - fn: 1684.0000 - accuracy: 0.7130 - precision: 0.6514 - recall: 0.9179 - auc: 0.8998 - prc: 0.9236 - val_loss: 0.6968 - val_tp: 76.0000 - val_fp: 18526.0000 - val_tn: 26962.0000 - val_fn: 5.0000 - val_accuracy: 0.5933 - val_precision: 0.0041 - val_recall: 0.9383 - val_auc: 0.9461 - val_prc: 0.5271
Epoch 3/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.4434 - tp: 19145.0000 - fp: 8327.0000 - tn: 11911.0000 - fn: 1577.0000 - accuracy: 0.7582 - precision: 0.6969 - recall: 0.9239 - auc: 0.9211 - prc: 0.9418 - val_loss: 0.5855 - val_tp: 76.0000 - val_fp: 13098.0000 - val_tn: 32390.0000 - val_fn: 5.0000 - val_accuracy: 0.7125 - val_precision: 0.0058 - val_recall: 0.9383 - val_auc: 0.9522 - val_prc: 0.6018
Epoch 4/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.3971 - tp: 18676.0000 - fp: 6939.0000 - tn: 13732.0000 - fn: 1613.0000 - accuracy: 0.7912 - precision: 0.7291 - recall: 0.9205 - auc: 0.9333 - prc: 0.9494 - val_loss: 0.4957 - val_tp: 74.0000 - val_fp: 8821.0000 - val_tn: 36667.0000 - val_fn: 7.0000 - val_accuracy: 0.8063 - val_precision: 0.0083 - val_recall: 0.9136 - val_auc: 0.9582 - val_prc: 0.6391
Epoch 5/1000
20/20 [==============================] - 1s 30ms/step - loss: 0.3539 - tp: 18791.0000 - fp: 5597.0000 - tn: 14895.0000 - fn: 1677.0000 - accuracy: 0.8224 - precision: 0.7705 - recall: 0.9181 - auc: 0.9425 - prc: 0.9574 - val_loss: 0.4256 - val_tp: 74.0000 - val_fp: 5917.0000 - val_tn: 39571.0000 - val_fn: 7.0000 - val_accuracy: 0.8700 - val_precision: 0.0124 - val_recall: 0.9136 - val_auc: 0.9627 - val_prc: 0.6553
Epoch 6/1000
20/20 [==============================] - 1s 30ms/step - loss: 0.3204 - tp: 18968.0000 - fp: 4538.0000 - tn: 15788.0000 - fn: 1666.0000 - accuracy: 0.8485 - precision: 0.8069 - recall: 0.9193 - auc: 0.9496 - prc: 0.9629 - val_loss: 0.3721 - val_tp: 74.0000 - val_fp: 4201.0000 - val_tn: 41287.0000 - val_fn: 7.0000 - val_accuracy: 0.9077 - val_precision: 0.0173 - val_recall: 0.9136 - val_auc: 0.9667 - val_prc: 0.6676
Epoch 7/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.2984 - tp: 18860.0000 - fp: 3840.0000 - tn: 16600.0000 - fn: 1660.0000 - accuracy: 0.8657 - precision: 0.8308 - recall: 0.9191 - auc: 0.9549 - prc: 0.9662 - val_loss: 0.3278 - val_tp: 74.0000 - val_fp: 3004.0000 - val_tn: 42484.0000 - val_fn: 7.0000 - val_accuracy: 0.9339 - val_precision: 0.0240 - val_recall: 0.9136 - val_auc: 0.9699 - val_prc: 0.6773
Epoch 8/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.2782 - tp: 18666.0000 - fp: 3317.0000 - tn: 17303.0000 - fn: 1674.0000 - accuracy: 0.8781 - precision: 0.8491 - recall: 0.9177 - auc: 0.9594 - prc: 0.9690 - val_loss: 0.2909 - val_tp: 74.0000 - val_fp: 2254.0000 - val_tn: 43234.0000 - val_fn: 7.0000 - val_accuracy: 0.9504 - val_precision: 0.0318 - val_recall: 0.9136 - val_auc: 0.9721 - val_prc: 0.6832
Epoch 9/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.2605 - tp: 18624.0000 - fp: 2839.0000 - tn: 17810.0000 - fn: 1687.0000 - accuracy: 0.8895 - precision: 0.8677 - recall: 0.9169 - auc: 0.9632 - prc: 0.9718 - val_loss: 0.2620 - val_tp: 74.0000 - val_fp: 1835.0000 - val_tn: 43653.0000 - val_fn: 7.0000 - val_accuracy: 0.9596 - val_precision: 0.0388 - val_recall: 0.9136 - val_auc: 0.9734 - val_prc: 0.6925
Epoch 10/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.2446 - tp: 19007.0000 - fp: 2353.0000 - tn: 17919.0000 - fn: 1681.0000 - accuracy: 0.9015 - precision: 0.8898 - recall: 0.9187 - auc: 0.9661 - prc: 0.9744 - val_loss: 0.2393 - val_tp: 75.0000 - val_fp: 1589.0000 - val_tn: 43899.0000 - val_fn: 6.0000 - val_accuracy: 0.9650 - val_precision: 0.0451 - val_recall: 0.9259 - val_auc: 0.9746 - val_prc: 0.6991
Epoch 11/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.2357 - tp: 18790.0000 - fp: 2209.0000 - tn: 18283.0000 - fn: 1678.0000 - accuracy: 0.9051 - precision: 0.8948 - recall: 0.9180 - auc: 0.9687 - prc: 0.9755 - val_loss: 0.2203 - val_tp: 75.0000 - val_fp: 1427.0000 - val_tn: 44061.0000 - val_fn: 6.0000 - val_accuracy: 0.9686 - val_precision: 0.0499 - val_recall: 0.9259 - val_auc: 0.9753 - val_prc: 0.7045
Epoch 12/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.2219 - tp: 18790.0000 - fp: 1963.0000 - tn: 18533.0000 - fn: 1674.0000 - accuracy: 0.9112 - precision: 0.9054 - recall: 0.9182 - auc: 0.9720 - prc: 0.9778 - val_loss: 0.2033 - val_tp: 75.0000 - val_fp: 1307.0000 - val_tn: 44181.0000 - val_fn: 6.0000 - val_accuracy: 0.9712 - val_precision: 0.0543 - val_recall: 0.9259 - val_auc: 0.9759 - val_prc: 0.7086
Epoch 13/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.2133 - tp: 18788.0000 - fp: 1833.0000 - tn: 18717.0000 - fn: 1622.0000 - accuracy: 0.9156 - precision: 0.9111 - recall: 0.9205 - auc: 0.9741 - prc: 0.9792 - val_loss: 0.1891 - val_tp: 75.0000 - val_fp: 1243.0000 - val_tn: 44245.0000 - val_fn: 6.0000 - val_accuracy: 0.9726 - val_precision: 0.0569 - val_recall: 0.9259 - val_auc: 0.9761 - val_prc: 0.7107
Epoch 14/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.2056 - tp: 18712.0000 - fp: 1702.0000 - tn: 18942.0000 - fn: 1604.0000 - accuracy: 0.9193 - precision: 0.9166 - recall: 0.9210 - auc: 0.9756 - prc: 0.9801 - val_loss: 0.1766 - val_tp: 75.0000 - val_fp: 1171.0000 - val_tn: 44317.0000 - val_fn: 6.0000 - val_accuracy: 0.9742 - val_precision: 0.0602 - val_recall: 0.9259 - val_auc: 0.9760 - val_prc: 0.7146
Epoch 15/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1949 - tp: 18902.0000 - fp: 1482.0000 - tn: 19001.0000 - fn: 1575.0000 - accuracy: 0.9254 - precision: 0.9273 - recall: 0.9231 - auc: 0.9782 - prc: 0.9822 - val_loss: 0.1659 - val_tp: 75.0000 - val_fp: 1144.0000 - val_tn: 44344.0000 - val_fn: 6.0000 - val_accuracy: 0.9748 - val_precision: 0.0615 - val_recall: 0.9259 - val_auc: 0.9760 - val_prc: 0.7149
Epoch 16/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1945 - tp: 18691.0000 - fp: 1533.0000 - tn: 19156.0000 - fn: 1580.0000 - accuracy: 0.9240 - precision: 0.9242 - recall: 0.9221 - auc: 0.9780 - prc: 0.9816 - val_loss: 0.1556 - val_tp: 75.0000 - val_fp: 1078.0000 - val_tn: 44410.0000 - val_fn: 6.0000 - val_accuracy: 0.9762 - val_precision: 0.0650 - val_recall: 0.9259 - val_auc: 0.9757 - val_prc: 0.7169
Epoch 17/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1848 - tp: 18904.0000 - fp: 1333.0000 - tn: 19156.0000 - fn: 1567.0000 - accuracy: 0.9292 - precision: 0.9341 - recall: 0.9235 - auc: 0.9801 - prc: 0.9834 - val_loss: 0.1474 - val_tp: 75.0000 - val_fp: 1061.0000 - val_tn: 44427.0000 - val_fn: 6.0000 - val_accuracy: 0.9766 - val_precision: 0.0660 - val_recall: 0.9259 - val_auc: 0.9755 - val_prc: 0.7233
Epoch 18/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1795 - tp: 18892.0000 - fp: 1332.0000 - tn: 19170.0000 - fn: 1566.0000 - accuracy: 0.9292 - precision: 0.9341 - recall: 0.9235 - auc: 0.9810 - prc: 0.9840 - val_loss: 0.1409 - val_tp: 75.0000 - val_fp: 1074.0000 - val_tn: 44414.0000 - val_fn: 6.0000 - val_accuracy: 0.9763 - val_precision: 0.0653 - val_recall: 0.9259 - val_auc: 0.9758 - val_prc: 0.7283
Epoch 19/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1777 - tp: 19003.0000 - fp: 1336.0000 - tn: 19109.0000 - fn: 1512.0000 - accuracy: 0.9305 - precision: 0.9343 - recall: 0.9263 - auc: 0.9815 - prc: 0.9844 - val_loss: 0.1338 - val_tp: 75.0000 - val_fp: 1035.0000 - val_tn: 44453.0000 - val_fn: 6.0000 - val_accuracy: 0.9772 - val_precision: 0.0676 - val_recall: 0.9259 - val_auc: 0.9756 - val_prc: 0.7286
Epoch 20/1000
20/20 [==============================] - 1s 31ms/step - loss: 0.1729 - tp: 18882.0000 - fp: 1274.0000 - tn: 19325.0000 - fn: 1479.0000 - accuracy: 0.9328 - precision: 0.9368 - recall: 0.9274 - auc: 0.9827 - prc: 0.9849 - val_loss: 0.1269 - val_tp: 75.0000 - val_fp: 997.0000 - val_tn: 44491.0000 - val_fn: 6.0000 - val_accuracy: 0.9780 - val_precision: 0.0700 - val_recall: 0.9259 - val_auc: 0.9757 - val_prc: 0.7233
Epoch 21/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.1660 - tp: 18989.0000 - fp: 1145.0000 - tn: 19319.0000 - fn: 1507.0000 - accuracy: 0.9353 - precision: 0.9431 - recall: 0.9265 - auc: 0.9840 - prc: 0.9862 - val_loss: 0.1218 - val_tp: 75.0000 - val_fp: 995.0000 - val_tn: 44493.0000 - val_fn: 6.0000 - val_accuracy: 0.9780 - val_precision: 0.0701 - val_recall: 0.9259 - val_auc: 0.9756 - val_prc: 0.7267
Epoch 22/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1626 - tp: 19009.0000 - fp: 1148.0000 - tn: 19349.0000 - fn: 1454.0000 - accuracy: 0.9365 - precision: 0.9430 - recall: 0.9289 - auc: 0.9847 - prc: 0.9866 - val_loss: 0.1173 - val_tp: 75.0000 - val_fp: 996.0000 - val_tn: 44492.0000 - val_fn: 6.0000 - val_accuracy: 0.9780 - val_precision: 0.0700 - val_recall: 0.9259 - val_auc: 0.9755 - val_prc: 0.7190
Epoch 23/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1578 - tp: 18958.0000 - fp: 1108.0000 - tn: 19419.0000 - fn: 1475.0000 - accuracy: 0.9369 - precision: 0.9448 - recall: 0.9278 - auc: 0.9853 - prc: 0.9871 - val_loss: 0.1134 - val_tp: 75.0000 - val_fp: 1001.0000 - val_tn: 44487.0000 - val_fn: 6.0000 - val_accuracy: 0.9779 - val_precision: 0.0697 - val_recall: 0.9259 - val_auc: 0.9759 - val_prc: 0.7199
Epoch 24/1000
20/20 [==============================] - 1s 30ms/step - loss: 0.1560 - tp: 19078.0000 - fp: 1074.0000 - tn: 19418.0000 - fn: 1390.0000 - accuracy: 0.9398 - precision: 0.9467 - recall: 0.9321 - auc: 0.9862 - prc: 0.9877 - val_loss: 0.1095 - val_tp: 75.0000 - val_fp: 1013.0000 - val_tn: 44475.0000 - val_fn: 6.0000 - val_accuracy: 0.9776 - val_precision: 0.0689 - val_recall: 0.9259 - val_auc: 0.9760 - val_prc: 0.7203
Epoch 25/1000
20/20 [==============================] - 1s 30ms/step - loss: 0.1526 - tp: 19222.0000 - fp: 1068.0000 - tn: 19256.0000 - fn: 1414.0000 - accuracy: 0.9394 - precision: 0.9474 - recall: 0.9315 - auc: 0.9865 - prc: 0.9882 - val_loss: 0.1054 - val_tp: 75.0000 - val_fp: 984.0000 - val_tn: 44504.0000 - val_fn: 6.0000 - val_accuracy: 0.9783 - val_precision: 0.0708 - val_recall: 0.9259 - val_auc: 0.9754 - val_prc: 0.7213
Epoch 26/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1504 - tp: 18992.0000 - fp: 1073.0000 - tn: 19475.0000 - fn: 1420.0000 - accuracy: 0.9391 - precision: 0.9465 - recall: 0.9304 - auc: 0.9869 - prc: 0.9881 - val_loss: 0.1024 - val_tp: 75.0000 - val_fp: 988.0000 - val_tn: 44500.0000 - val_fn: 6.0000 - val_accuracy: 0.9782 - val_precision: 0.0706 - val_recall: 0.9259 - val_auc: 0.9759 - val_prc: 0.7215
Epoch 27/1000
20/20 [==============================] - 1s 29ms/step - loss: 0.1464 - tp: 19140.0000 - fp: 974.0000 - tn: 19433.0000 - fn: 1413.0000 - accuracy: 0.9417 - precision: 0.9516 - recall: 0.9313 - auc: 0.9877 - prc: 0.9889 - val_loss: 0.1001 - val_tp: 75.0000 - val_fp: 994.0000 - val_tn: 44494.0000 - val_fn: 6.0000 - val_accuracy: 0.9781 - val_precision: 0.0702 - val_recall: 0.9259 - val_auc: 0.9763 - val_prc: 0.7218
Epoch 28/1000
20/20 [==============================] - 1s 28ms/step - loss: 0.1436 - tp: 19103.0000 - fp: 978.0000 - tn: 19526.0000 - fn: 1353.0000 - accuracy: 0.9431 - precision: 0.9513 - recall: 0.9339 - auc: 0.9884 - prc: 0.9894 - val_loss: 0.0974 - val_tp: 75.0000 - val_fp: 986.0000 - val_tn: 44502.0000 - val_fn: 6.0000 - val_accuracy: 0.9782 - val_precision: 0.0707 - val_recall: 0.9259 - val_auc: 0.9757 - val_prc: 0.7216
Epoch 29/1000
18/20 [==========================>...] - ETA: 0s - loss: 0.1445 - tp: 17095.0000 - fp: 886.0000 - tn: 17596.0000 - fn: 1287.0000 - accuracy: 0.9411 - precision: 0.9507 - recall: 0.9300 - auc: 0.9883 - prc: 0.9891Restoring model weights from the end of the best epoch: 19.
20/20 [==============================] - 1s 30ms/step - loss: 0.1440 - tp: 18978.0000 - fp: 976.0000 - tn: 19592.0000 - fn: 1414.0000 - accuracy: 0.9417 - precision: 0.9511 - recall: 0.9307 - auc: 0.9884 - prc: 0.9891 - val_loss: 0.0939 - val_tp: 75.0000 - val_fp: 951.0000 - val_tn: 44537.0000 - val_fn: 6.0000 - val_accuracy: 0.9790 - val_precision: 0.0731 - val_recall: 0.9259 - val_auc: 0.9757 - val_prc: 0.7220
Epoch 29: early stopping

Re-check training history

plot_metrics(resampled_history)

Evaluate metrics

train_predictions_resampled = resampled_model.predict(train_features, batch_size=BATCH_SIZE)
test_predictions_resampled = resampled_model.predict(test_features, batch_size=BATCH_SIZE)

90/90 [==============================] - 0s 1ms/step
28/28 [==============================] - 0s 1ms/step

resampled_results = resampled_model.evaluate(test_features, test_labels,
                                             batch_size=BATCH_SIZE, verbose=0)
for name, value in zip(resampled_model.metrics_names, resampled_results):
  print(name, ': ', value)
print()

plot_cm(test_labels, test_predictions_resampled)

loss :  0.13431145250797272
tp :  87.0
fp :  1381.0
tn :  55484.0
fn :  10.0
accuracy :  0.9755802154541016
precision :  0.05926430597901344
recall :  0.8969072103500366
auc :  0.9665377140045166
prc :  0.7062013745307922

Legitimate Transactions Detected (True Negatives):  55484
Legitimate Transactions Incorrectly Detected (False Positives):  1381
Fraudulent Transactions Missed (False Negatives):  10
Fraudulent Transactions Detected (True Positives):  87
Total Fraudulent Transactions:  97

Plot the ROC

plot_roc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_roc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')

plot_roc("Train Weighted", train_labels, train_predictions_weighted, color=colors[1])
plot_roc("Test Weighted", test_labels, test_predictions_weighted, color=colors[1], linestyle='--')

plot_roc("Train Resampled", train_labels, train_predictions_resampled, color=colors[2])
plot_roc("Test Resampled", test_labels, test_predictions_resampled, color=colors[2], linestyle='--')
plt.legend(loc='lower right');

Plot the AUPRC

plot_prc("Train Baseline", train_labels, train_predictions_baseline, color=colors[0])
plot_prc("Test Baseline", test_labels, test_predictions_baseline, color=colors[0], linestyle='--')

plot_prc("Train Weighted", train_labels, train_predictions_weighted, color=colors[1])
plot_prc("Test Weighted", test_labels, test_predictions_weighted, color=colors[1], linestyle='--')

plot_prc("Train Resampled", train_labels, train_predictions_resampled, color=colors[2])
plot_prc("Test Resampled", test_labels, test_predictions_resampled, color=colors[2], linestyle='--')
plt.legend(loc='lower right');

Applying this tutorial to your problem

Imbalanced data classification is an inherently difficult task since there are so few samples to learn from. You should always start with the data first and do your best to collect as many samples as possible and give substantial thought to what features may be relevant so the model can get the most out of your minority class. At some point your model may struggle to improve and yield the results you want, so it is important to keep in mind the context of your problem and the trade offs between different types of errors.