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Classification on imbalanced data

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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
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.

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 Ammount'] = 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.

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)

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")

png

png

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.

Read more:

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.

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])
array([[0.3673761 ],
       [0.35600176],
       [0.60139984],
       [0.42065838],
       [0.37041035],
       [0.27554348],
       [0.39560333],
       [0.5962162 ],
       [0.6676472 ],
       [0.47435313]], 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: 0.6497

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])
array([[0.00085616],
       [0.0043528 ],
       [0.00127403],
       [0.00196918],
       [0.00238743],
       [0.01523864],
       [0.00139776],
       [0.01105964],
       [0.00072914],
       [0.00378807]], 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: 0.0164

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)

png

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 [==============================] - 3s 17ms/step - loss: 0.0131 - tp: 90.0000 - fp: 31.0000 - tn: 227426.0000 - fn: 298.0000 - accuracy: 0.9986 - precision: 0.7438 - recall: 0.2320 - auc: 0.7283 - prc: 0.2674 - val_loss: 0.0088 - val_tp: 0.0000e+00 - val_fp: 0.0000e+00 - val_tn: 45481.0000 - val_fn: 88.0000 - val_accuracy: 0.9981 - val_precision: 0.0000e+00 - val_recall: 0.0000e+00 - val_auc: 0.8910 - val_prc: 0.6002
Epoch 2/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0086 - tp: 73.0000 - fp: 23.0000 - tn: 181953.0000 - fn: 227.0000 - accuracy: 0.9986 - precision: 0.7604 - recall: 0.2433 - auc: 0.7955 - prc: 0.3433 - val_loss: 0.0058 - val_tp: 31.0000 - val_fp: 6.0000 - val_tn: 45475.0000 - val_fn: 57.0000 - val_accuracy: 0.9986 - val_precision: 0.8378 - val_recall: 0.3523 - val_auc: 0.9145 - val_prc: 0.6818
Epoch 3/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0071 - tp: 115.0000 - fp: 22.0000 - tn: 181954.0000 - fn: 185.0000 - accuracy: 0.9989 - precision: 0.8394 - recall: 0.3833 - auc: 0.8513 - prc: 0.4569 - val_loss: 0.0048 - val_tp: 43.0000 - val_fp: 7.0000 - val_tn: 45474.0000 - val_fn: 45.0000 - val_accuracy: 0.9989 - val_precision: 0.8600 - val_recall: 0.4886 - val_auc: 0.9315 - val_prc: 0.7302
Epoch 4/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0063 - tp: 121.0000 - fp: 24.0000 - tn: 181952.0000 - fn: 179.0000 - accuracy: 0.9989 - precision: 0.8345 - recall: 0.4033 - auc: 0.8797 - prc: 0.5420 - val_loss: 0.0044 - val_tp: 53.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 35.0000 - val_accuracy: 0.9990 - val_precision: 0.8413 - val_recall: 0.6023 - val_auc: 0.9315 - val_prc: 0.7347
Epoch 5/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0057 - tp: 157.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 143.0000 - accuracy: 0.9991 - precision: 0.8533 - recall: 0.5233 - auc: 0.8925 - prc: 0.5852 - val_loss: 0.0042 - val_tp: 55.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 33.0000 - val_accuracy: 0.9990 - val_precision: 0.8333 - val_recall: 0.6250 - val_auc: 0.9372 - val_prc: 0.7623
Epoch 6/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0050 - tp: 158.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 142.0000 - accuracy: 0.9991 - precision: 0.8634 - recall: 0.5267 - auc: 0.9166 - prc: 0.6520 - val_loss: 0.0040 - val_tp: 56.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 32.0000 - val_accuracy: 0.9991 - val_precision: 0.8358 - val_recall: 0.6364 - val_auc: 0.9429 - val_prc: 0.7732
Epoch 7/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0054 - tp: 157.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 143.0000 - accuracy: 0.9990 - precision: 0.8351 - recall: 0.5233 - auc: 0.9066 - prc: 0.5991 - val_loss: 0.0039 - val_tp: 54.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 34.0000 - val_accuracy: 0.9990 - val_precision: 0.8438 - val_recall: 0.6136 - val_auc: 0.9429 - val_prc: 0.7902
Epoch 8/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0048 - tp: 162.0000 - fp: 36.0000 - tn: 181940.0000 - fn: 138.0000 - accuracy: 0.9990 - precision: 0.8182 - recall: 0.5400 - auc: 0.9036 - prc: 0.6601 - val_loss: 0.0037 - val_tp: 55.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 33.0000 - val_accuracy: 0.9991 - val_precision: 0.8462 - val_recall: 0.6250 - val_auc: 0.9429 - val_prc: 0.8039
Epoch 9/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0045 - tp: 169.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 131.0000 - accuracy: 0.9991 - precision: 0.8535 - recall: 0.5633 - auc: 0.9137 - prc: 0.6753 - val_loss: 0.0035 - val_tp: 64.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 24.0000 - val_accuracy: 0.9993 - val_precision: 0.8649 - val_recall: 0.7273 - val_auc: 0.9486 - val_prc: 0.8152
Epoch 10/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0047 - tp: 167.0000 - fp: 33.0000 - tn: 181943.0000 - fn: 133.0000 - accuracy: 0.9991 - precision: 0.8350 - recall: 0.5567 - auc: 0.9122 - prc: 0.6616 - val_loss: 0.0034 - val_tp: 66.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 22.0000 - val_accuracy: 0.9993 - val_precision: 0.8684 - val_recall: 0.7500 - val_auc: 0.9485 - val_prc: 0.8199
Epoch 11/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0045 - tp: 177.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 123.0000 - accuracy: 0.9992 - precision: 0.8510 - recall: 0.5900 - auc: 0.9206 - prc: 0.6849 - val_loss: 0.0033 - val_tp: 66.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 22.0000 - val_accuracy: 0.9993 - val_precision: 0.8684 - val_recall: 0.7500 - val_auc: 0.9486 - val_prc: 0.8273
Epoch 12/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0041 - tp: 181.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 119.0000 - accuracy: 0.9992 - precision: 0.8786 - recall: 0.6033 - auc: 0.9190 - prc: 0.7070 - val_loss: 0.0032 - val_tp: 67.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 21.0000 - val_accuracy: 0.9993 - val_precision: 0.8701 - val_recall: 0.7614 - val_auc: 0.9486 - val_prc: 0.8283
Epoch 13/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0044 - tp: 170.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 130.0000 - accuracy: 0.9991 - precision: 0.8416 - recall: 0.5667 - auc: 0.9189 - prc: 0.6625 - val_loss: 0.0032 - val_tp: 67.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 21.0000 - val_accuracy: 0.9993 - val_precision: 0.8701 - val_recall: 0.7614 - val_auc: 0.9485 - val_prc: 0.8298
Epoch 14/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0041 - tp: 177.0000 - fp: 33.0000 - tn: 181943.0000 - fn: 123.0000 - accuracy: 0.9991 - precision: 0.8429 - recall: 0.5900 - auc: 0.9323 - prc: 0.6980 - val_loss: 0.0031 - val_tp: 68.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8718 - val_recall: 0.7727 - val_auc: 0.9486 - val_prc: 0.8352
Epoch 15/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0040 - tp: 180.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 120.0000 - accuracy: 0.9992 - precision: 0.8738 - recall: 0.6000 - auc: 0.9291 - prc: 0.7266 - val_loss: 0.0031 - val_tp: 71.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8659 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8368
Epoch 16/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0041 - tp: 177.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 123.0000 - accuracy: 0.9992 - precision: 0.8592 - recall: 0.5900 - auc: 0.9157 - prc: 0.6905 - val_loss: 0.0031 - val_tp: 68.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 20.0000 - val_accuracy: 0.9993 - val_precision: 0.8608 - val_recall: 0.7727 - val_auc: 0.9486 - val_prc: 0.8380
Epoch 17/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0041 - tp: 182.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 118.0000 - accuracy: 0.9992 - precision: 0.8585 - recall: 0.6067 - auc: 0.9224 - prc: 0.6989 - val_loss: 0.0030 - val_tp: 69.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 19.0000 - val_accuracy: 0.9993 - val_precision: 0.8625 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8386
Epoch 18/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0039 - tp: 182.0000 - fp: 21.0000 - tn: 181955.0000 - fn: 118.0000 - accuracy: 0.9992 - precision: 0.8966 - recall: 0.6067 - auc: 0.9208 - prc: 0.7208 - val_loss: 0.0030 - val_tp: 71.0000 - val_fp: 12.0000 - val_tn: 45469.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8554 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8402
Epoch 19/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0041 - tp: 178.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 122.0000 - accuracy: 0.9992 - precision: 0.8476 - recall: 0.5933 - auc: 0.9307 - prc: 0.6853 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8750 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8441
Epoch 20/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0039 - tp: 176.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 124.0000 - accuracy: 0.9992 - precision: 0.8756 - recall: 0.5867 - auc: 0.9158 - prc: 0.7067 - val_loss: 0.0030 - val_tp: 71.0000 - val_fp: 12.0000 - val_tn: 45469.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8554 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8400
Epoch 21/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0039 - tp: 182.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 118.0000 - accuracy: 0.9992 - precision: 0.8585 - recall: 0.6067 - auc: 0.9275 - prc: 0.7128 - val_loss: 0.0030 - val_tp: 71.0000 - val_fp: 12.0000 - val_tn: 45469.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8554 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8407
Epoch 22/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0042 - tp: 167.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 133.0000 - accuracy: 0.9991 - precision: 0.8392 - recall: 0.5567 - auc: 0.9308 - prc: 0.6904 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8765 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8445
Epoch 23/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0039 - tp: 185.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8645 - recall: 0.6167 - auc: 0.9225 - prc: 0.7176 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8463
Epoch 24/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 186.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 114.0000 - accuracy: 0.9992 - precision: 0.8692 - recall: 0.6200 - auc: 0.9276 - prc: 0.7350 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 17.0000 - val_accuracy: 0.9995 - val_precision: 0.8987 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8458
Epoch 25/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0040 - tp: 178.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 122.0000 - accuracy: 0.9992 - precision: 0.8641 - recall: 0.5933 - auc: 0.9291 - prc: 0.7050 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8464
Epoch 26/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 187.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8618 - recall: 0.6233 - auc: 0.9343 - prc: 0.7460 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8659 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8466
Epoch 27/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0038 - tp: 187.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8821 - recall: 0.6233 - auc: 0.9242 - prc: 0.7149 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 12.0000 - val_tn: 45469.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8554 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8457
Epoch 28/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0036 - tp: 198.0000 - fp: 34.0000 - tn: 181942.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8534 - recall: 0.6600 - auc: 0.9359 - prc: 0.7386 - val_loss: 0.0029 - val_tp: 69.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8961 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8488
Epoch 29/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 179.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 121.0000 - accuracy: 0.9992 - precision: 0.8775 - recall: 0.5967 - auc: 0.9343 - prc: 0.7502 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8765 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8470
Epoch 30/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0037 - tp: 186.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 114.0000 - accuracy: 0.9992 - precision: 0.8651 - recall: 0.6200 - auc: 0.9309 - prc: 0.7295 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8765 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8463
Epoch 31/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0036 - tp: 190.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 110.0000 - accuracy: 0.9993 - precision: 0.8837 - recall: 0.6333 - auc: 0.9209 - prc: 0.7331 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8468
Epoch 32/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 183.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 117.0000 - accuracy: 0.9992 - precision: 0.8756 - recall: 0.6100 - auc: 0.9276 - prc: 0.7292 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8659 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8460
Epoch 33/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0039 - tp: 176.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 124.0000 - accuracy: 0.9992 - precision: 0.8544 - recall: 0.5867 - auc: 0.9209 - prc: 0.6988 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8477
Epoch 34/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 182.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 118.0000 - accuracy: 0.9992 - precision: 0.8585 - recall: 0.6067 - auc: 0.9326 - prc: 0.7344 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8659 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8466
Epoch 35/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0038 - tp: 187.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8698 - recall: 0.6233 - auc: 0.9259 - prc: 0.7212 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8489
Epoch 36/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 191.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 109.0000 - accuracy: 0.9993 - precision: 0.8802 - recall: 0.6367 - auc: 0.9326 - prc: 0.7360 - val_loss: 0.0028 - val_tp: 69.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8846 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8517
Epoch 37/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 177.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 123.0000 - accuracy: 0.9992 - precision: 0.8592 - recall: 0.5900 - auc: 0.9292 - prc: 0.7441 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8488
Epoch 38/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 194.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 106.0000 - accuracy: 0.9992 - precision: 0.8622 - recall: 0.6467 - auc: 0.9376 - prc: 0.7547 - val_loss: 0.0029 - val_tp: 69.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8846 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8524
Epoch 39/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 191.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8682 - recall: 0.6367 - auc: 0.9377 - prc: 0.7484 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8510
Epoch 40/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 174.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 126.0000 - accuracy: 0.9991 - precision: 0.8571 - recall: 0.5800 - auc: 0.9226 - prc: 0.7251 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8765 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8496
Epoch 41/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 185.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8810 - recall: 0.6167 - auc: 0.9343 - prc: 0.7545 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8765 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8500
Epoch 42/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 189.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8670 - recall: 0.6300 - auc: 0.9325 - prc: 0.7329 - val_loss: 0.0028 - val_tp: 69.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8961 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8524
Epoch 43/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0038 - tp: 179.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 121.0000 - accuracy: 0.9992 - precision: 0.8565 - recall: 0.5967 - auc: 0.9292 - prc: 0.7203 - val_loss: 0.0028 - val_tp: 69.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8961 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8540
Epoch 44/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 185.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8605 - recall: 0.6167 - auc: 0.9309 - prc: 0.7426 - val_loss: 0.0028 - val_tp: 71.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 17.0000 - val_accuracy: 0.9995 - val_precision: 0.8987 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8535
Epoch 45/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 183.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 117.0000 - accuracy: 0.9992 - precision: 0.8756 - recall: 0.6100 - auc: 0.9358 - prc: 0.7326 - val_loss: 0.0029 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8514
Epoch 46/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0035 - tp: 190.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 110.0000 - accuracy: 0.9992 - precision: 0.8676 - recall: 0.6333 - auc: 0.9326 - prc: 0.7380 - val_loss: 0.0029 - val_tp: 69.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8846 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8535
Epoch 47/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0036 - tp: 181.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 119.0000 - accuracy: 0.9992 - precision: 0.8660 - recall: 0.6033 - auc: 0.9393 - prc: 0.7377 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8539
Epoch 48/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0037 - tp: 189.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8750 - recall: 0.6300 - auc: 0.9343 - prc: 0.7321 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8508
Epoch 49/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0035 - tp: 185.0000 - fp: 22.0000 - tn: 181954.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8937 - recall: 0.6167 - auc: 0.9376 - prc: 0.7449 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8533
Epoch 50/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 188.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 112.0000 - accuracy: 0.9992 - precision: 0.8785 - recall: 0.6267 - auc: 0.9359 - prc: 0.7460 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8551
Epoch 51/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 191.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8604 - recall: 0.6367 - auc: 0.9375 - prc: 0.7310 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8538
Epoch 52/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 186.0000 - fp: 24.0000 - tn: 181952.0000 - fn: 114.0000 - accuracy: 0.9992 - precision: 0.8857 - recall: 0.6200 - auc: 0.9309 - prc: 0.7459 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8549
Epoch 53/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0034 - tp: 185.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8565 - recall: 0.6167 - auc: 0.9393 - prc: 0.7542 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8551
Epoch 54/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 176.0000 - fp: 36.0000 - tn: 181940.0000 - fn: 124.0000 - accuracy: 0.9991 - precision: 0.8302 - recall: 0.5867 - auc: 0.9342 - prc: 0.7158 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8567
Epoch 55/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 198.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8800 - recall: 0.6600 - auc: 0.9275 - prc: 0.7405 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8563
Epoch 56/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 189.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8630 - recall: 0.6300 - auc: 0.9376 - prc: 0.7492 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8554
Epoch 57/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 191.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 109.0000 - accuracy: 0.9993 - precision: 0.8761 - recall: 0.6367 - auc: 0.9376 - prc: 0.7500 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8556
Epoch 58/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 199.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8652 - recall: 0.6633 - auc: 0.9376 - prc: 0.7427 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8545
Epoch 59/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 179.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 121.0000 - accuracy: 0.9992 - precision: 0.8647 - recall: 0.5967 - auc: 0.9309 - prc: 0.7359 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8572
Epoch 60/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 192.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 108.0000 - accuracy: 0.9992 - precision: 0.8610 - recall: 0.6400 - auc: 0.9427 - prc: 0.7627 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8574
Epoch 61/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0032 - tp: 196.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8869 - recall: 0.6533 - auc: 0.9393 - prc: 0.7707 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8579
Epoch 62/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0038 - tp: 185.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 115.0000 - accuracy: 0.9992 - precision: 0.8525 - recall: 0.6167 - auc: 0.9292 - prc: 0.7110 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8575
Epoch 63/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0034 - tp: 190.0000 - fp: 20.0000 - tn: 181956.0000 - fn: 110.0000 - accuracy: 0.9993 - precision: 0.9048 - recall: 0.6333 - auc: 0.9310 - prc: 0.7612 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8565
Epoch 64/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0034 - tp: 195.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8705 - recall: 0.6500 - auc: 0.9343 - prc: 0.7484 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8579
Epoch 65/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0038 - tp: 179.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 121.0000 - accuracy: 0.9992 - precision: 0.8606 - recall: 0.5967 - auc: 0.9392 - prc: 0.7198 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8577
Epoch 66/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 194.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8818 - recall: 0.6467 - auc: 0.9410 - prc: 0.7776 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8550
Epoch 67/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0031 - tp: 203.0000 - fp: 23.0000 - tn: 181953.0000 - fn: 97.0000 - accuracy: 0.9993 - precision: 0.8982 - recall: 0.6767 - auc: 0.9460 - prc: 0.7723 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8593
Epoch 68/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0031 - tp: 197.0000 - fp: 22.0000 - tn: 181954.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8995 - recall: 0.6567 - auc: 0.9393 - prc: 0.7738 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8574
Epoch 69/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 190.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 110.0000 - accuracy: 0.9993 - precision: 0.8837 - recall: 0.6333 - auc: 0.9359 - prc: 0.7415 - val_loss: 0.0029 - val_tp: 73.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8795 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8544
Epoch 70/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 191.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8682 - recall: 0.6367 - auc: 0.9410 - prc: 0.7520 - val_loss: 0.0028 - val_tp: 71.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 17.0000 - val_accuracy: 0.9994 - val_precision: 0.8875 - val_recall: 0.8068 - val_auc: 0.9486 - val_prc: 0.8570
Epoch 71/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 188.0000 - fp: 23.0000 - tn: 181953.0000 - fn: 112.0000 - accuracy: 0.9993 - precision: 0.8910 - recall: 0.6267 - auc: 0.9343 - prc: 0.7540 - val_loss: 0.0029 - val_tp: 73.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8795 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8549
Epoch 72/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0036 - tp: 189.0000 - fp: 33.0000 - tn: 181943.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8514 - recall: 0.6300 - auc: 0.9309 - prc: 0.7316 - val_loss: 0.0029 - val_tp: 73.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8902 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8570
Epoch 73/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 197.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8717 - recall: 0.6567 - auc: 0.9376 - prc: 0.7599 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8861 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8573
Epoch 74/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 194.0000 - fp: 35.0000 - tn: 181941.0000 - fn: 106.0000 - accuracy: 0.9992 - precision: 0.8472 - recall: 0.6467 - auc: 0.9427 - prc: 0.7755 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8574
Epoch 75/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0035 - tp: 182.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 118.0000 - accuracy: 0.9992 - precision: 0.8626 - recall: 0.6067 - auc: 0.9293 - prc: 0.7400 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8573
Epoch 76/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 194.0000 - fp: 24.0000 - tn: 181952.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8899 - recall: 0.6467 - auc: 0.9376 - prc: 0.7653 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8570
Epoch 77/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 204.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 96.0000 - accuracy: 0.9993 - precision: 0.8793 - recall: 0.6800 - auc: 0.9475 - prc: 0.7588 - val_loss: 0.0028 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8594
Epoch 78/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0037 - tp: 172.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 128.0000 - accuracy: 0.9991 - precision: 0.8643 - recall: 0.5733 - auc: 0.9275 - prc: 0.7356 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8573
Epoch 79/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0033 - tp: 191.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8565 - recall: 0.6367 - auc: 0.9426 - prc: 0.7641 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8564
Epoch 80/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 184.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 116.0000 - accuracy: 0.9992 - precision: 0.8679 - recall: 0.6133 - auc: 0.9493 - prc: 0.7617 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8565
Epoch 81/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 196.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8750 - recall: 0.6533 - auc: 0.9392 - prc: 0.7553 - val_loss: 0.0029 - val_tp: 69.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.8961 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8573
Epoch 82/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 192.0000 - fp: 30.0000 - tn: 181946.0000 - fn: 108.0000 - accuracy: 0.9992 - precision: 0.8649 - recall: 0.6400 - auc: 0.9410 - prc: 0.7590 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8578
Epoch 83/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 194.0000 - fp: 27.0000 - tn: 181949.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8778 - recall: 0.6467 - auc: 0.9476 - prc: 0.7682 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 16.0000 - val_accuracy: 0.9994 - val_precision: 0.8780 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8579
Epoch 84/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 195.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 105.0000 - accuracy: 0.9993 - precision: 0.8744 - recall: 0.6500 - auc: 0.9393 - prc: 0.7555 - val_loss: 0.0030 - val_tp: 73.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8795 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8559
Epoch 85/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 196.0000 - fp: 26.0000 - tn: 181950.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8829 - recall: 0.6533 - auc: 0.9459 - prc: 0.7552 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8578
Epoch 86/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0033 - tp: 194.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 106.0000 - accuracy: 0.9993 - precision: 0.8858 - recall: 0.6467 - auc: 0.9392 - prc: 0.7643 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8581
Epoch 87/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0033 - tp: 189.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8710 - recall: 0.6300 - auc: 0.9459 - prc: 0.7549 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8596
Epoch 88/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 187.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 113.0000 - accuracy: 0.9992 - precision: 0.8821 - recall: 0.6233 - auc: 0.9492 - prc: 0.7707 - val_loss: 0.0030 - val_tp: 73.0000 - val_fp: 13.0000 - val_tn: 45468.0000 - val_fn: 15.0000 - val_accuracy: 0.9994 - val_precision: 0.8488 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8552
Epoch 89/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 199.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 101.0000 - accuracy: 0.9993 - precision: 0.8767 - recall: 0.6633 - auc: 0.9426 - prc: 0.7671 - val_loss: 0.0029 - val_tp: 73.0000 - val_fp: 10.0000 - val_tn: 45471.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8795 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8580
Epoch 90/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 189.0000 - fp: 28.0000 - tn: 181948.0000 - fn: 111.0000 - accuracy: 0.9992 - precision: 0.8710 - recall: 0.6300 - auc: 0.9408 - prc: 0.7518 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8601
Epoch 91/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 196.0000 - fp: 21.0000 - tn: 181955.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.9032 - recall: 0.6533 - auc: 0.9426 - prc: 0.7775 - val_loss: 0.0030 - val_tp: 73.0000 - val_fp: 11.0000 - val_tn: 45470.0000 - val_fn: 15.0000 - val_accuracy: 0.9994 - val_precision: 0.8690 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8576
Epoch 92/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0033 - tp: 198.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 102.0000 - accuracy: 0.9993 - precision: 0.8646 - recall: 0.6600 - auc: 0.9475 - prc: 0.7590 - val_loss: 0.0029 - val_tp: 69.0000 - val_fp: 7.0000 - val_tn: 45474.0000 - val_fn: 19.0000 - val_accuracy: 0.9994 - val_precision: 0.9079 - val_recall: 0.7841 - val_auc: 0.9486 - val_prc: 0.8609
Epoch 93/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 191.0000 - fp: 23.0000 - tn: 181953.0000 - fn: 109.0000 - accuracy: 0.9993 - precision: 0.8925 - recall: 0.6367 - auc: 0.9325 - prc: 0.7718 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8574
Epoch 94/100
90/90 [==============================] - 1s 8ms/step - loss: 0.0032 - tp: 197.0000 - fp: 24.0000 - tn: 181952.0000 - fn: 103.0000 - accuracy: 0.9993 - precision: 0.8914 - recall: 0.6567 - auc: 0.9375 - prc: 0.7699 - val_loss: 0.0030 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8573
Epoch 95/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 195.0000 - fp: 32.0000 - tn: 181944.0000 - fn: 105.0000 - accuracy: 0.9992 - precision: 0.8590 - recall: 0.6500 - auc: 0.9477 - prc: 0.7725 - val_loss: 0.0030 - val_tp: 72.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.8889 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8584
Epoch 96/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0030 - tp: 201.0000 - fp: 24.0000 - tn: 181952.0000 - fn: 99.0000 - accuracy: 0.9993 - precision: 0.8933 - recall: 0.6700 - auc: 0.9410 - prc: 0.7920 - val_loss: 0.0029 - val_tp: 72.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 16.0000 - val_accuracy: 0.9995 - val_precision: 0.9000 - val_recall: 0.8182 - val_auc: 0.9486 - val_prc: 0.8595
Epoch 97/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0032 - tp: 191.0000 - fp: 29.0000 - tn: 181947.0000 - fn: 109.0000 - accuracy: 0.9992 - precision: 0.8682 - recall: 0.6367 - auc: 0.9509 - prc: 0.7784 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8589
Epoch 98/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0031 - tp: 206.0000 - fp: 21.0000 - tn: 181955.0000 - fn: 94.0000 - accuracy: 0.9994 - precision: 0.9075 - recall: 0.6867 - auc: 0.9493 - prc: 0.7891 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8591
Epoch 99/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0035 - tp: 179.0000 - fp: 25.0000 - tn: 181951.0000 - fn: 121.0000 - accuracy: 0.9992 - precision: 0.8775 - recall: 0.5967 - auc: 0.9408 - prc: 0.7521 - val_loss: 0.0030 - val_tp: 73.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 15.0000 - val_accuracy: 0.9995 - val_precision: 0.8902 - val_recall: 0.8295 - val_auc: 0.9486 - val_prc: 0.8583
Epoch 100/100
90/90 [==============================] - 1s 7ms/step - loss: 0.0034 - tp: 196.0000 - fp: 31.0000 - tn: 181945.0000 - fn: 104.0000 - accuracy: 0.9993 - precision: 0.8634 - recall: 0.6533 - auc: 0.9508 - prc: 0.7584 - val_loss: 0.0029 - val_tp: 70.0000 - val_fp: 8.0000 - val_tn: 45473.0000 - val_fn: 18.0000 - val_accuracy: 0.9994 - val_precision: 0.8974 - val_recall: 0.7955 - val_auc: 0.9486 - val_prc: 0.8592

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)

png

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)
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 :  0.0030180125031620264
tp :  82.0
fp :  5.0
tn :  56853.0
fn :  22.0
accuracy :  0.9995260238647461
precision :  0.9425287246704102
recall :  0.7884615659713745
auc :  0.9372756481170654
prc :  0.8531103730201721

Legitimate Transactions Detected (True Negatives):  56853
Legitimate Transactions Incorrectly Detected (False Positives):  5
Fraudulent Transactions Missed (False Negatives):  22
Fraudulent Transactions Detected (True Positives):  82
Total Fraudulent Transactions:  104

png

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');

png

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('Recall')
    plt.ylabel('Precision')
    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');

png

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.

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 [==============================] - 3s 17ms/step - loss: 2.4908 - tp: 117.0000 - fp: 127.0000 - tn: 238707.0000 - fn: 287.0000 - accuracy: 0.9983 - precision: 0.4795 - recall: 0.2896 - auc: 0.7329 - prc: 0.2830 - val_loss: 0.0091 - val_tp: 25.0000 - val_fp: 9.0000 - val_tn: 45472.0000 - val_fn: 63.0000 - val_accuracy: 0.9984 - val_precision: 0.7353 - val_recall: 0.2841 - val_auc: 0.9311 - val_prc: 0.4668
Epoch 2/100
90/90 [==============================] - 1s 8ms/step - loss: 1.1350 - tp: 128.0000 - fp: 367.0000 - tn: 181609.0000 - fn: 172.0000 - accuracy: 0.9970 - precision: 0.2586 - recall: 0.4267 - auc: 0.8473 - prc: 0.3033 - val_loss: 0.0105 - val_tp: 63.0000 - val_fp: 22.0000 - val_tn: 45459.0000 - val_fn: 25.0000 - val_accuracy: 0.9990 - val_precision: 0.7412 - val_recall: 0.7159 - val_auc: 0.9546 - val_prc: 0.6863
Epoch 3/100
90/90 [==============================] - 1s 7ms/step - loss: 0.7347 - tp: 181.0000 - fp: 1105.0000 - tn: 180871.0000 - fn: 119.0000 - accuracy: 0.9933 - precision: 0.1407 - recall: 0.6033 - auc: 0.8961 - prc: 0.3683 - val_loss: 0.0166 - val_tp: 75.0000 - val_fp: 59.0000 - val_tn: 45422.0000 - val_fn: 13.0000 - val_accuracy: 0.9984 - val_precision: 0.5597 - val_recall: 0.8523 - val_auc: 0.9531 - val_prc: 0.7303
Epoch 4/100
90/90 [==============================] - 1s 8ms/step - loss: 0.5927 - tp: 204.0000 - fp: 2153.0000 - tn: 179823.0000 - fn: 96.0000 - accuracy: 0.9877 - precision: 0.0866 - recall: 0.6800 - auc: 0.9051 - prc: 0.3409 - val_loss: 0.0255 - val_tp: 79.0000 - val_fp: 207.0000 - val_tn: 45274.0000 - val_fn: 9.0000 - val_accuracy: 0.9953 - val_precision: 0.2762 - val_recall: 0.8977 - val_auc: 0.9580 - val_prc: 0.7195
Epoch 5/100
90/90 [==============================] - 1s 8ms/step - loss: 0.4751 - tp: 230.0000 - fp: 2891.0000 - tn: 179085.0000 - fn: 70.0000 - accuracy: 0.9838 - precision: 0.0737 - recall: 0.7667 - auc: 0.9168 - prc: 0.2923 - val_loss: 0.0344 - val_tp: 79.0000 - val_fp: 376.0000 - val_tn: 45105.0000 - val_fn: 9.0000 - val_accuracy: 0.9916 - val_precision: 0.1736 - val_recall: 0.8977 - val_auc: 0.9577 - val_prc: 0.6827
Epoch 6/100
90/90 [==============================] - 1s 7ms/step - loss: 0.3777 - tp: 239.0000 - fp: 3813.0000 - tn: 178163.0000 - fn: 61.0000 - accuracy: 0.9787 - precision: 0.0590 - recall: 0.7967 - auc: 0.9352 - prc: 0.2408 - val_loss: 0.0441 - val_tp: 80.0000 - val_fp: 502.0000 - val_tn: 44979.0000 - val_fn: 8.0000 - val_accuracy: 0.9888 - val_precision: 0.1375 - val_recall: 0.9091 - val_auc: 0.9602 - val_prc: 0.6813
Epoch 7/100
90/90 [==============================] - 1s 7ms/step - loss: 0.3936 - tp: 245.0000 - fp: 4649.0000 - tn: 177327.0000 - fn: 55.0000 - accuracy: 0.9742 - precision: 0.0501 - recall: 0.8167 - auc: 0.9277 - prc: 0.2108 - val_loss: 0.0540 - val_tp: 80.0000 - val_fp: 630.0000 - val_tn: 44851.0000 - val_fn: 8.0000 - val_accuracy: 0.9860 - val_precision: 0.1127 - val_recall: 0.9091 - val_auc: 0.9610 - val_prc: 0.6825
Epoch 8/100
90/90 [==============================] - 1s 7ms/step - loss: 0.3975 - tp: 243.0000 - fp: 5322.0000 - tn: 176654.0000 - fn: 57.0000 - accuracy: 0.9705 - precision: 0.0437 - recall: 0.8100 - auc: 0.9232 - prc: 0.2013 - val_loss: 0.0623 - val_tp: 80.0000 - val_fp: 719.0000 - val_tn: 44762.0000 - val_fn: 8.0000 - val_accuracy: 0.9840 - val_precision: 0.1001 - val_recall: 0.9091 - val_auc: 0.9614 - val_prc: 0.6878
Epoch 9/100
90/90 [==============================] - 1s 7ms/step - loss: 0.3066 - tp: 254.0000 - fp: 5795.0000 - tn: 176181.0000 - fn: 46.0000 - accuracy: 0.9680 - precision: 0.0420 - recall: 0.8467 - auc: 0.9470 - prc: 0.1891 - val_loss: 0.0672 - val_tp: 80.0000 - val_fp: 758.0000 - val_tn: 44723.0000 - val_fn: 8.0000 - val_accuracy: 0.9832 - val_precision: 0.0955 - val_recall: 0.9091 - val_auc: 0.9631 - val_prc: 0.6807
Epoch 10/100
90/90 [==============================] - 1s 8ms/step - loss: 0.3111 - tp: 254.0000 - fp: 5995.0000 - tn: 175981.0000 - fn: 46.0000 - accuracy: 0.9669 - precision: 0.0406 - recall: 0.8467 - auc: 0.9473 - prc: 0.1843 - val_loss: 0.0722 - val_tp: 80.0000 - val_fp: 806.0000 - val_tn: 44675.0000 - val_fn: 8.0000 - val_accuracy: 0.9821 - val_precision: 0.0903 - val_recall: 0.9091 - val_auc: 0.9649 - val_prc: 0.6524
Epoch 11/100
90/90 [==============================] - 1s 8ms/step - loss: 0.3300 - tp: 251.0000 - fp: 6288.0000 - tn: 175688.0000 - fn: 49.0000 - accuracy: 0.9652 - precision: 0.0384 - recall: 0.8367 - auc: 0.9402 - prc: 0.1755 - val_loss: 0.0767 - val_tp: 80.0000 - val_fp: 843.0000 - val_tn: 44638.0000 - val_fn: 8.0000 - val_accuracy: 0.9813 - val_precision: 0.0867 - val_recall: 0.9091 - val_auc: 0.9652 - val_prc: 0.6501
Epoch 12/100
90/90 [==============================] - 1s 8ms/step - loss: 0.3178 - tp: 254.0000 - fp: 6563.0000 - tn: 175413.0000 - fn: 46.0000 - accuracy: 0.9637 - precision: 0.0373 - recall: 0.8467 - auc: 0.9421 - prc: 0.1784 - val_loss: 0.0796 - val_tp: 80.0000 - val_fp: 875.0000 - val_tn: 44606.0000 - val_fn: 8.0000 - val_accuracy: 0.9806 - val_precision: 0.0838 - val_recall: 0.9091 - val_auc: 0.9661 - val_prc: 0.6500
Epoch 13/100
89/90 [============================>.] - ETA: 0s - loss: 0.2418 - tp: 264.0000 - fp: 6410.0000 - tn: 175562.0000 - fn: 36.0000 - accuracy: 0.9646 - precision: 0.0396 - recall: 0.8800 - auc: 0.9620 - prc: 0.1929Restoring model weights from the end of the best epoch: 3.
90/90 [==============================] - 1s 8ms/step - loss: 0.2417 - tp: 264.0000 - fp: 6410.0000 - tn: 175566.0000 - fn: 36.0000 - accuracy: 0.9646 - precision: 0.0396 - recall: 0.8800 - auc: 0.9620 - prc: 0.1929 - val_loss: 0.0791 - val_tp: 80.0000 - val_fp: 866.0000 - val_tn: 44615.0000 - val_fn: 8.0000 - val_accuracy: 0.9808 - val_precision: 0.0846 - val_recall: 0.9091 - val_auc: 0.9673 - val_prc: 0.6443
Epoch 13: early stopping

Check training history

plot_metrics(weighted_history)

png

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)
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 :  0.015673985704779625
tp :  88.0
fp :  64.0
tn :  56794.0
fn :  16.0
accuracy :  0.9985955357551575
precision :  0.5789473652839661
recall :  0.8461538553237915
auc :  0.9661166071891785
prc :  0.7658032178878784

Legitimate Transactions Detected (True Negatives):  56794
Legitimate Transactions Incorrectly Detected (False Positives):  64
Fraudulent Transactions Missed (False Negatives):  16
Fraudulent Transactions Detected (True Positives):  88
Total Fraudulent Transactions:  104

png

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');

png

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');

png

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
(181976, 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
(363952, 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:
 [-1.70995646e+00  6.07169433e-02 -4.04871449e+00  2.40588467e+00
  3.27081930e-01 -1.17238978e+00 -1.09074333e+00  5.57028845e-01
 -2.90711834e+00 -4.55481109e+00  3.65557488e+00 -4.64769769e+00
  1.02148437e+00 -5.00000000e+00 -6.47163060e-01 -5.00000000e+00
 -5.00000000e+00 -1.89067352e+00  2.36913527e+00  3.35002702e-01
  1.16080677e+00  1.71862788e+00  2.98862257e+00 -1.93354761e-01
  2.33545393e+00 -2.13017771e-03  2.55719520e+00  1.14788658e-02
  1.39790139e+00]

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())
0.4990234375

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.

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 [==============================] - 11s 34ms/step - loss: 0.5088 - tp: 230540.0000 - fp: 87893.0000 - tn: 253318.0000 - fn: 54555.0000 - accuracy: 0.7726 - precision: 0.7240 - recall: 0.8086 - auc: 0.8724 - prc: 0.8948 - val_loss: 0.2745 - val_tp: 80.0000 - val_fp: 1324.0000 - val_tn: 44157.0000 - val_fn: 8.0000 - val_accuracy: 0.9708 - val_precision: 0.0570 - val_recall: 0.9091 - val_auc: 0.9607 - val_prc: 0.7477
Epoch 2/100
278/278 [==============================] - 9s 31ms/step - loss: 0.2251 - tp: 255911.0000 - fp: 18957.0000 - tn: 265276.0000 - fn: 29200.0000 - accuracy: 0.9154 - precision: 0.9310 - recall: 0.8976 - auc: 0.9673 - prc: 0.9748 - val_loss: 0.1428 - val_tp: 81.0000 - val_fp: 760.0000 - val_tn: 44721.0000 - val_fn: 7.0000 - val_accuracy: 0.9832 - val_precision: 0.0963 - val_recall: 0.9205 - val_auc: 0.9745 - val_prc: 0.7576
Epoch 3/100
278/278 [==============================] - 9s 32ms/step - loss: 0.1657 - tp: 261422.0000 - fp: 10411.0000 - tn: 274107.0000 - fn: 23404.0000 - accuracy: 0.9406 - precision: 0.9617 - recall: 0.9178 - auc: 0.9824 - prc: 0.9856 - val_loss: 0.0971 - val_tp: 79.0000 - val_fp: 703.0000 - val_tn: 44778.0000 - val_fn: 9.0000 - val_accuracy: 0.9844 - val_precision: 0.1010 - val_recall: 0.8977 - val_auc: 0.9770 - val_prc: 0.7608
Epoch 4/100
278/278 [==============================] - 9s 31ms/step - loss: 0.1414 - tp: 264138.0000 - fp: 8560.0000 - tn: 275567.0000 - fn: 21079.0000 - accuracy: 0.9479 - precision: 0.9686 - recall: 0.9261 - auc: 0.9875 - prc: 0.9892 - val_loss: 0.0822 - val_tp: 79.0000 - val_fp: 720.0000 - val_tn: 44761.0000 - val_fn: 9.0000 - val_accuracy: 0.9840 - val_precision: 0.0989 - val_recall: 0.8977 - val_auc: 0.9785 - val_prc: 0.7223
Epoch 5/100
278/278 [==============================] - 9s 31ms/step - loss: 0.1254 - tp: 265494.0000 - fp: 7921.0000 - tn: 277121.0000 - fn: 18808.0000 - accuracy: 0.9531 - precision: 0.9710 - recall: 0.9338 - auc: 0.9906 - prc: 0.9915 - val_loss: 0.0726 - val_tp: 79.0000 - val_fp: 693.0000 - val_tn: 44788.0000 - val_fn: 9.0000 - val_accuracy: 0.9846 - val_precision: 0.1023 - val_recall: 0.8977 - val_auc: 0.9790 - val_prc: 0.7068
Epoch 6/100
278/278 [==============================] - 8s 31ms/step - loss: 0.1150 - tp: 267476.0000 - fp: 7403.0000 - tn: 277131.0000 - fn: 17334.0000 - accuracy: 0.9566 - precision: 0.9731 - recall: 0.9391 - auc: 0.9925 - prc: 0.9929 - val_loss: 0.0651 - val_tp: 79.0000 - val_fp: 647.0000 - val_tn: 44834.0000 - val_fn: 9.0000 - val_accuracy: 0.9856 - val_precision: 0.1088 - val_recall: 0.8977 - val_auc: 0.9797 - val_prc: 0.7061
Epoch 7/100
278/278 [==============================] - 8s 31ms/step - loss: 0.1065 - tp: 268558.0000 - fp: 7008.0000 - tn: 277671.0000 - fn: 16107.0000 - accuracy: 0.9594 - precision: 0.9746 - recall: 0.9434 - auc: 0.9938 - prc: 0.9939 - val_loss: 0.0602 - val_tp: 79.0000 - val_fp: 616.0000 - val_tn: 44865.0000 - val_fn: 9.0000 - val_accuracy: 0.9863 - val_precision: 0.1137 - val_recall: 0.8977 - val_auc: 0.9795 - val_prc: 0.7053
Epoch 8/100
278/278 [==============================] - 9s 31ms/step - loss: 0.1010 - tp: 269426.0000 - fp: 6824.0000 - tn: 277689.0000 - fn: 15405.0000 - accuracy: 0.9610 - precision: 0.9753 - recall: 0.9459 - auc: 0.9945 - prc: 0.9944 - val_loss: 0.0556 - val_tp: 79.0000 - val_fp: 580.0000 - val_tn: 44901.0000 - val_fn: 9.0000 - val_accuracy: 0.9871 - val_precision: 0.1199 - val_recall: 0.8977 - val_auc: 0.9782 - val_prc: 0.7055
Epoch 9/100
278/278 [==============================] - 9s 31ms/step - loss: 0.0956 - tp: 269858.0000 - fp: 6522.0000 - tn: 278173.0000 - fn: 14791.0000 - accuracy: 0.9626 - precision: 0.9764 - recall: 0.9480 - auc: 0.9952 - prc: 0.9950 - val_loss: 0.0516 - val_tp: 79.0000 - val_fp: 550.0000 - val_tn: 44931.0000 - val_fn: 9.0000 - val_accuracy: 0.9877 - val_precision: 0.1256 - val_recall: 0.8977 - val_auc: 0.9748 - val_prc: 0.6982
Epoch 10/100
278/278 [==============================] - 9s 33ms/step - loss: 0.0906 - tp: 270484.0000 - fp: 6297.0000 - tn: 278534.0000 - fn: 14029.0000 - accuracy: 0.9643 - precision: 0.9772 - recall: 0.9507 - auc: 0.9957 - prc: 0.9954 - val_loss: 0.0480 - val_tp: 79.0000 - val_fp: 533.0000 - val_tn: 44948.0000 - val_fn: 9.0000 - val_accuracy: 0.9881 - val_precision: 0.1291 - val_recall: 0.8977 - val_auc: 0.9711 - val_prc: 0.6974
Epoch 11/100
278/278 [==============================] - 9s 32ms/step - loss: 0.0872 - tp: 271073.0000 - fp: 6184.0000 - tn: 278743.0000 - fn: 13344.0000 - accuracy: 0.9657 - precision: 0.9777 - recall: 0.9531 - auc: 0.9959 - prc: 0.9955 - val_loss: 0.0451 - val_tp: 79.0000 - val_fp: 499.0000 - val_tn: 44982.0000 - val_fn: 9.0000 - val_accuracy: 0.9889 - val_precision: 0.1367 - val_recall: 0.8977 - val_auc: 0.9718 - val_prc: 0.6978
Epoch 12/100
278/278 [==============================] - 9s 31ms/step - loss: 0.0845 - tp: 272241.0000 - fp: 6027.0000 - tn: 278427.0000 - fn: 12649.0000 - accuracy: 0.9672 - precision: 0.9783 - recall: 0.9556 - auc: 0.9961 - prc: 0.9957 - val_loss: 0.0429 - val_tp: 80.0000 - val_fp: 491.0000 - val_tn: 44990.0000 - val_fn: 8.0000 - val_accuracy: 0.9890 - val_precision: 0.1401 - val_recall: 0.9091 - val_auc: 0.9724 - val_prc: 0.6985
Epoch 13/100
278/278 [==============================] - ETA: 0s - loss: 0.0819 - tp: 272096.0000 - fp: 6016.0000 - tn: 279208.0000 - fn: 12024.0000 - accuracy: 0.9683 - precision: 0.9784 - recall: 0.9577 - auc: 0.9964 - prc: 0.9959Restoring model weights from the end of the best epoch: 3.
278/278 [==============================] - 9s 31ms/step - loss: 0.0819 - tp: 272096.0000 - fp: 6016.0000 - tn: 279208.0000 - fn: 12024.0000 - accuracy: 0.9683 - precision: 0.9784 - recall: 0.9577 - auc: 0.9964 - prc: 0.9959 - val_loss: 0.0414 - val_tp: 80.0000 - val_fp: 481.0000 - val_tn: 45000.0000 - val_fn: 8.0000 - val_accuracy: 0.9893 - val_precision: 0.1426 - val_recall: 0.9091 - val_auc: 0.9725 - val_prc: 0.6919
Epoch 13: 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)

png

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 82ms/step - loss: 1.3690 - tp: 8842.0000 - fp: 12784.0000 - tn: 53027.0000 - fn: 11876.0000 - accuracy: 0.7150 - precision: 0.4089 - recall: 0.4268 - auc: 0.7595 - prc: 0.5091 - val_loss: 0.8506 - val_tp: 67.0000 - val_fp: 29685.0000 - val_tn: 15796.0000 - val_fn: 21.0000 - val_accuracy: 0.3481 - val_precision: 0.0023 - val_recall: 0.7614 - val_auc: 0.6300 - val_prc: 0.0062
Epoch 2/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.8734 - tp: 13189.0000 - fp: 12148.0000 - tn: 8360.0000 - fn: 7263.0000 - accuracy: 0.5261 - precision: 0.5205 - recall: 0.6449 - auc: 0.6060 - prc: 0.7169 - val_loss: 0.7935 - val_tp: 84.0000 - val_fp: 27319.0000 - val_tn: 18162.0000 - val_fn: 4.0000 - val_accuracy: 0.4004 - val_precision: 0.0031 - val_recall: 0.9545 - val_auc: 0.9085 - val_prc: 0.2791
Epoch 3/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.6591 - tp: 15609.0000 - fp: 10735.0000 - tn: 9709.0000 - fn: 4907.0000 - accuracy: 0.6181 - precision: 0.5925 - recall: 0.7608 - auc: 0.7480 - prc: 0.8226 - val_loss: 0.7176 - val_tp: 82.0000 - val_fp: 22854.0000 - val_tn: 22627.0000 - val_fn: 6.0000 - val_accuracy: 0.4983 - val_precision: 0.0036 - val_recall: 0.9318 - val_auc: 0.9326 - val_prc: 0.5680
Epoch 4/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.5539 - tp: 16763.0000 - fp: 9451.0000 - tn: 11067.0000 - fn: 3679.0000 - accuracy: 0.6794 - precision: 0.6395 - recall: 0.8200 - auc: 0.8230 - prc: 0.8754 - val_loss: 0.6429 - val_tp: 81.0000 - val_fp: 17203.0000 - val_tn: 28278.0000 - val_fn: 7.0000 - val_accuracy: 0.6223 - val_precision: 0.0047 - val_recall: 0.9205 - val_auc: 0.9382 - val_prc: 0.6592
Epoch 5/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.4977 - tp: 17232.0000 - fp: 8173.0000 - tn: 12322.0000 - fn: 3233.0000 - accuracy: 0.7215 - precision: 0.6783 - recall: 0.8420 - auc: 0.8566 - prc: 0.8994 - val_loss: 0.5758 - val_tp: 81.0000 - val_fp: 12096.0000 - val_tn: 33385.0000 - val_fn: 7.0000 - val_accuracy: 0.7344 - val_precision: 0.0067 - val_recall: 0.9205 - val_auc: 0.9430 - val_prc: 0.6902
Epoch 6/1000
20/20 [==============================] - 1s 39ms/step - loss: 0.4476 - tp: 17521.0000 - fp: 6825.0000 - tn: 13574.0000 - fn: 3040.0000 - accuracy: 0.7592 - precision: 0.7197 - recall: 0.8521 - auc: 0.8820 - prc: 0.9173 - val_loss: 0.5188 - val_tp: 81.0000 - val_fp: 8455.0000 - val_tn: 37026.0000 - val_fn: 7.0000 - val_accuracy: 0.8143 - val_precision: 0.0095 - val_recall: 0.9205 - val_auc: 0.9474 - val_prc: 0.7144
Epoch 7/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.4159 - tp: 17568.0000 - fp: 5807.0000 - tn: 14655.0000 - fn: 2930.0000 - accuracy: 0.7867 - precision: 0.7516 - recall: 0.8571 - auc: 0.8961 - prc: 0.9275 - val_loss: 0.4714 - val_tp: 81.0000 - val_fp: 6057.0000 - val_tn: 39424.0000 - val_fn: 7.0000 - val_accuracy: 0.8669 - val_precision: 0.0132 - val_recall: 0.9205 - val_auc: 0.9504 - val_prc: 0.7150
Epoch 8/1000
20/20 [==============================] - 1s 40ms/step - loss: 0.3878 - tp: 17820.0000 - fp: 4889.0000 - tn: 15384.0000 - fn: 2867.0000 - accuracy: 0.8106 - precision: 0.7847 - recall: 0.8614 - auc: 0.9084 - prc: 0.9366 - val_loss: 0.4308 - val_tp: 80.0000 - val_fp: 4423.0000 - val_tn: 41058.0000 - val_fn: 8.0000 - val_accuracy: 0.9028 - val_precision: 0.0178 - val_recall: 0.9091 - val_auc: 0.9521 - val_prc: 0.7212
Epoch 9/1000
20/20 [==============================] - 1s 40ms/step - loss: 0.3640 - tp: 17911.0000 - fp: 4232.0000 - tn: 16145.0000 - fn: 2672.0000 - accuracy: 0.8314 - precision: 0.8089 - recall: 0.8702 - auc: 0.9195 - prc: 0.9435 - val_loss: 0.3956 - val_tp: 80.0000 - val_fp: 3289.0000 - val_tn: 42192.0000 - val_fn: 8.0000 - val_accuracy: 0.9276 - val_precision: 0.0237 - val_recall: 0.9091 - val_auc: 0.9533 - val_prc: 0.7290
Epoch 10/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.3349 - tp: 18031.0000 - fp: 3595.0000 - tn: 16870.0000 - fn: 2464.0000 - accuracy: 0.8521 - precision: 0.8338 - recall: 0.8798 - auc: 0.9315 - prc: 0.9515 - val_loss: 0.3639 - val_tp: 80.0000 - val_fp: 2497.0000 - val_tn: 42984.0000 - val_fn: 8.0000 - val_accuracy: 0.9450 - val_precision: 0.0310 - val_recall: 0.9091 - val_auc: 0.9548 - val_prc: 0.7271
Epoch 11/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.3226 - tp: 18061.0000 - fp: 3143.0000 - tn: 17279.0000 - fn: 2477.0000 - accuracy: 0.8628 - precision: 0.8518 - recall: 0.8794 - auc: 0.9351 - prc: 0.9540 - val_loss: 0.3371 - val_tp: 80.0000 - val_fp: 2002.0000 - val_tn: 43479.0000 - val_fn: 8.0000 - val_accuracy: 0.9559 - val_precision: 0.0384 - val_recall: 0.9091 - val_auc: 0.9563 - val_prc: 0.7383
Epoch 12/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.3051 - tp: 18156.0000 - fp: 2760.0000 - tn: 17604.0000 - fn: 2440.0000 - accuracy: 0.8730 - precision: 0.8680 - recall: 0.8815 - auc: 0.9409 - prc: 0.9580 - val_loss: 0.3144 - val_tp: 80.0000 - val_fp: 1694.0000 - val_tn: 43787.0000 - val_fn: 8.0000 - val_accuracy: 0.9627 - val_precision: 0.0451 - val_recall: 0.9091 - val_auc: 0.9575 - val_prc: 0.7333
Epoch 13/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2989 - tp: 17991.0000 - fp: 2630.0000 - tn: 17929.0000 - fn: 2410.0000 - accuracy: 0.8770 - precision: 0.8725 - recall: 0.8819 - auc: 0.9431 - prc: 0.9586 - val_loss: 0.2940 - val_tp: 80.0000 - val_fp: 1454.0000 - val_tn: 44027.0000 - val_fn: 8.0000 - val_accuracy: 0.9679 - val_precision: 0.0522 - val_recall: 0.9091 - val_auc: 0.9589 - val_prc: 0.7397
Epoch 14/1000
20/20 [==============================] - 1s 39ms/step - loss: 0.2803 - tp: 18224.0000 - fp: 2312.0000 - tn: 18068.0000 - fn: 2356.0000 - accuracy: 0.8860 - precision: 0.8874 - recall: 0.8855 - auc: 0.9496 - prc: 0.9634 - val_loss: 0.2759 - val_tp: 80.0000 - val_fp: 1319.0000 - val_tn: 44162.0000 - val_fn: 8.0000 - val_accuracy: 0.9709 - val_precision: 0.0572 - val_recall: 0.9091 - val_auc: 0.9603 - val_prc: 0.7473
Epoch 15/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.2720 - tp: 18148.0000 - fp: 2078.0000 - tn: 18372.0000 - fn: 2362.0000 - accuracy: 0.8916 - precision: 0.8973 - recall: 0.8848 - auc: 0.9523 - prc: 0.9647 - val_loss: 0.2599 - val_tp: 80.0000 - val_fp: 1201.0000 - val_tn: 44280.0000 - val_fn: 8.0000 - val_accuracy: 0.9735 - val_precision: 0.0625 - val_recall: 0.9091 - val_auc: 0.9619 - val_prc: 0.7508
Epoch 16/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.2597 - tp: 18246.0000 - fp: 1900.0000 - tn: 18545.0000 - fn: 2269.0000 - accuracy: 0.8982 - precision: 0.9057 - recall: 0.8894 - auc: 0.9568 - prc: 0.9680 - val_loss: 0.2450 - val_tp: 80.0000 - val_fp: 1102.0000 - val_tn: 44379.0000 - val_fn: 8.0000 - val_accuracy: 0.9756 - val_precision: 0.0677 - val_recall: 0.9091 - val_auc: 0.9632 - val_prc: 0.7551
Epoch 17/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2521 - tp: 18191.0000 - fp: 1700.0000 - tn: 18784.0000 - fn: 2285.0000 - accuracy: 0.9027 - precision: 0.9145 - recall: 0.8884 - auc: 0.9592 - prc: 0.9691 - val_loss: 0.2322 - val_tp: 80.0000 - val_fp: 1042.0000 - val_tn: 44439.0000 - val_fn: 8.0000 - val_accuracy: 0.9770 - val_precision: 0.0713 - val_recall: 0.9091 - val_auc: 0.9645 - val_prc: 0.7542
Epoch 18/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.2451 - tp: 18311.0000 - fp: 1624.0000 - tn: 18736.0000 - fn: 2289.0000 - accuracy: 0.9045 - precision: 0.9185 - recall: 0.8889 - auc: 0.9606 - prc: 0.9706 - val_loss: 0.2209 - val_tp: 80.0000 - val_fp: 993.0000 - val_tn: 44488.0000 - val_fn: 8.0000 - val_accuracy: 0.9780 - val_precision: 0.0746 - val_recall: 0.9091 - val_auc: 0.9654 - val_prc: 0.7565
Epoch 19/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2398 - tp: 18368.0000 - fp: 1523.0000 - tn: 18859.0000 - fn: 2210.0000 - accuracy: 0.9089 - precision: 0.9234 - recall: 0.8926 - auc: 0.9629 - prc: 0.9719 - val_loss: 0.2107 - val_tp: 80.0000 - val_fp: 951.0000 - val_tn: 44530.0000 - val_fn: 8.0000 - val_accuracy: 0.9790 - val_precision: 0.0776 - val_recall: 0.9091 - val_auc: 0.9661 - val_prc: 0.7590
Epoch 20/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.2301 - tp: 18391.0000 - fp: 1391.0000 - tn: 19017.0000 - fn: 2161.0000 - accuracy: 0.9133 - precision: 0.9297 - recall: 0.8949 - auc: 0.9655 - prc: 0.9737 - val_loss: 0.2017 - val_tp: 80.0000 - val_fp: 918.0000 - val_tn: 44563.0000 - val_fn: 8.0000 - val_accuracy: 0.9797 - val_precision: 0.0802 - val_recall: 0.9091 - val_auc: 0.9673 - val_prc: 0.7596
Epoch 21/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2288 - tp: 18311.0000 - fp: 1344.0000 - tn: 19153.0000 - fn: 2152.0000 - accuracy: 0.9146 - precision: 0.9316 - recall: 0.8948 - auc: 0.9663 - prc: 0.9738 - val_loss: 0.1924 - val_tp: 80.0000 - val_fp: 893.0000 - val_tn: 44588.0000 - val_fn: 8.0000 - val_accuracy: 0.9802 - val_precision: 0.0822 - val_recall: 0.9091 - val_auc: 0.9684 - val_prc: 0.7604
Epoch 22/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2178 - tp: 18505.0000 - fp: 1193.0000 - tn: 19162.0000 - fn: 2100.0000 - accuracy: 0.9196 - precision: 0.9394 - recall: 0.8981 - auc: 0.9691 - prc: 0.9764 - val_loss: 0.1836 - val_tp: 80.0000 - val_fp: 854.0000 - val_tn: 44627.0000 - val_fn: 8.0000 - val_accuracy: 0.9811 - val_precision: 0.0857 - val_recall: 0.9091 - val_auc: 0.9695 - val_prc: 0.7606
Epoch 23/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2118 - tp: 18459.0000 - fp: 1173.0000 - tn: 19289.0000 - fn: 2039.0000 - accuracy: 0.9216 - precision: 0.9403 - recall: 0.9005 - auc: 0.9708 - prc: 0.9773 - val_loss: 0.1757 - val_tp: 81.0000 - val_fp: 848.0000 - val_tn: 44633.0000 - val_fn: 7.0000 - val_accuracy: 0.9812 - val_precision: 0.0872 - val_recall: 0.9205 - val_auc: 0.9702 - val_prc: 0.7610
Epoch 24/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2081 - tp: 18643.0000 - fp: 1146.0000 - tn: 19209.0000 - fn: 1962.0000 - accuracy: 0.9241 - precision: 0.9421 - recall: 0.9048 - auc: 0.9725 - prc: 0.9787 - val_loss: 0.1677 - val_tp: 81.0000 - val_fp: 818.0000 - val_tn: 44663.0000 - val_fn: 7.0000 - val_accuracy: 0.9819 - val_precision: 0.0901 - val_recall: 0.9205 - val_auc: 0.9711 - val_prc: 0.7629
Epoch 25/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.2020 - tp: 18600.0000 - fp: 1069.0000 - tn: 19308.0000 - fn: 1983.0000 - accuracy: 0.9255 - precision: 0.9457 - recall: 0.9037 - auc: 0.9739 - prc: 0.9796 - val_loss: 0.1609 - val_tp: 81.0000 - val_fp: 811.0000 - val_tn: 44670.0000 - val_fn: 7.0000 - val_accuracy: 0.9820 - val_precision: 0.0908 - val_recall: 0.9205 - val_auc: 0.9717 - val_prc: 0.7633
Epoch 26/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.1964 - tp: 18548.0000 - fp: 1001.0000 - tn: 19529.0000 - fn: 1882.0000 - accuracy: 0.9296 - precision: 0.9488 - recall: 0.9079 - auc: 0.9755 - prc: 0.9805 - val_loss: 0.1537 - val_tp: 81.0000 - val_fp: 779.0000 - val_tn: 44702.0000 - val_fn: 7.0000 - val_accuracy: 0.9828 - val_precision: 0.0942 - val_recall: 0.9205 - val_auc: 0.9726 - val_prc: 0.7570
Epoch 27/1000
20/20 [==============================] - 1s 38ms/step - loss: 0.1915 - tp: 18618.0000 - fp: 946.0000 - tn: 19568.0000 - fn: 1828.0000 - accuracy: 0.9323 - precision: 0.9516 - recall: 0.9106 - auc: 0.9766 - prc: 0.9815 - val_loss: 0.1478 - val_tp: 81.0000 - val_fp: 768.0000 - val_tn: 44713.0000 - val_fn: 7.0000 - val_accuracy: 0.9830 - val_precision: 0.0954 - val_recall: 0.9205 - val_auc: 0.9732 - val_prc: 0.7571
Epoch 28/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.1903 - tp: 18731.0000 - fp: 920.0000 - tn: 19487.0000 - fn: 1822.0000 - accuracy: 0.9331 - precision: 0.9532 - recall: 0.9114 - auc: 0.9766 - prc: 0.9815 - val_loss: 0.1422 - val_tp: 81.0000 - val_fp: 763.0000 - val_tn: 44718.0000 - val_fn: 7.0000 - val_accuracy: 0.9831 - val_precision: 0.0960 - val_recall: 0.9205 - val_auc: 0.9738 - val_prc: 0.7571
Epoch 29/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.1868 - tp: 18519.0000 - fp: 929.0000 - tn: 19714.0000 - fn: 1798.0000 - accuracy: 0.9334 - precision: 0.9522 - recall: 0.9115 - auc: 0.9776 - prc: 0.9819 - val_loss: 0.1369 - val_tp: 81.0000 - val_fp: 745.0000 - val_tn: 44736.0000 - val_fn: 7.0000 - val_accuracy: 0.9835 - val_precision: 0.0981 - val_recall: 0.9205 - val_auc: 0.9741 - val_prc: 0.7573
Epoch 30/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.1806 - tp: 18708.0000 - fp: 877.0000 - tn: 19617.0000 - fn: 1758.0000 - accuracy: 0.9357 - precision: 0.9552 - recall: 0.9141 - auc: 0.9791 - prc: 0.9832 - val_loss: 0.1324 - val_tp: 80.0000 - val_fp: 743.0000 - val_tn: 44738.0000 - val_fn: 8.0000 - val_accuracy: 0.9835 - val_precision: 0.0972 - val_recall: 0.9091 - val_auc: 0.9742 - val_prc: 0.7571
Epoch 31/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.1742 - tp: 18474.0000 - fp: 800.0000 - tn: 19976.0000 - fn: 1710.0000 - accuracy: 0.9387 - precision: 0.9585 - recall: 0.9153 - auc: 0.9807 - prc: 0.9841 - val_loss: 0.1276 - val_tp: 80.0000 - val_fp: 723.0000 - val_tn: 44758.0000 - val_fn: 8.0000 - val_accuracy: 0.9840 - val_precision: 0.0996 - val_recall: 0.9091 - val_auc: 0.9746 - val_prc: 0.7573
Epoch 32/1000
20/20 [==============================] - 1s 36ms/step - loss: 0.1741 - tp: 18801.0000 - fp: 799.0000 - tn: 19630.0000 - fn: 1730.0000 - accuracy: 0.9383 - precision: 0.9592 - recall: 0.9157 - auc: 0.9805 - prc: 0.9846 - val_loss: 0.1229 - val_tp: 80.0000 - val_fp: 702.0000 - val_tn: 44779.0000 - val_fn: 8.0000 - val_accuracy: 0.9844 - val_precision: 0.1023 - val_recall: 0.9091 - val_auc: 0.9749 - val_prc: 0.7573
Epoch 33/1000
20/20 [==============================] - 1s 37ms/step - loss: 0.1712 - tp: 18747.0000 - fp: 761.0000 - tn: 19759.0000 - fn: 1693.0000 - accuracy: 0.9401 - precision: 0.9610 - recall: 0.9172 - auc: 0.9812 - prc: 0.9847 - val_loss: 0.1195 - val_tp: 80.0000 - val_fp: 700.0000 - val_tn: 44781.0000 - val_fn: 8.0000 - val_accuracy: 0.9845 - val_precision: 0.1026 - val_recall: 0.9091 - val_auc: 0.9755 - val_prc: 0.7570
Epoch 34/1000
20/20 [==============================] - 1s 39ms/step - loss: 0.1696 - tp: 18751.0000 - fp: 757.0000 - tn: 19694.0000 - fn: 1758.0000 - accuracy: 0.9386 - precision: 0.9612 - recall: 0.9143 - auc: 0.9814 - prc: 0.9849 - val_loss: 0.1164 - val_tp: 80.0000 - val_fp: 703.0000 - val_tn: 44778.0000 - val_fn: 8.0000 - val_accuracy: 0.9844 - val_precision: 0.1022 - val_recall: 0.9091 - val_auc: 0.9757 - val_prc: 0.7572
Epoch 35/1000
20/20 [==============================] - ETA: 0s - loss: 0.1651 - tp: 18897.0000 - fp: 768.0000 - tn: 19603.0000 - fn: 1692.0000 - accuracy: 0.9399 - precision: 0.9609 - recall: 0.9178 - auc: 0.9825 - prc: 0.9857Restoring model weights from the end of the best epoch: 25.
20/20 [==============================] - 1s 39ms/step - loss: 0.1651 - tp: 18897.0000 - fp: 768.0000 - tn: 19603.0000 - fn: 1692.0000 - accuracy: 0.9399 - precision: 0.9609 - recall: 0.9178 - auc: 0.9825 - prc: 0.9857 - val_loss: 0.1134 - val_tp: 79.0000 - val_fp: 712.0000 - val_tn: 44769.0000 - val_fn: 9.0000 - val_accuracy: 0.9842 - val_precision: 0.0999 - val_recall: 0.8977 - val_auc: 0.9757 - val_prc: 0.7614
Epoch 35: early stopping

Re-check training history

plot_metrics(resampled_history)

png

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)
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 :  0.16031159460544586
tp :  93.0
fp :  1035.0
tn :  55823.0
fn :  11.0
accuracy :  0.9816368818283081
precision :  0.08244680613279343
recall :  0.8942307829856873
auc :  0.9773780703544617
prc :  0.7749922275543213

Legitimate Transactions Detected (True Negatives):  55823
Legitimate Transactions Incorrectly Detected (False Positives):  1035
Fraudulent Transactions Missed (False Negatives):  11
Fraudulent Transactions Detected (True Positives):  93
Total Fraudulent Transactions:  104

png

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');

png

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');

png

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.