# Logistic regression loss function (log loss).

If the last layer in your network applies a sigmoid to create a binary classification, how do you measure if the result is any good?

This code shows how to calculate the loss of a single training sample when the last layer in your neural network apllies a sigmoid function to create a binary classification.

If you are here just for the code, grab this and strip the comments:

def log_loss(act, target): """ target == 0 -> -math.log(1 - act) target == 1 -> -math.log(act) """ return -target * math.log(act) - (1 - target) * math.log(1 - act)

## Behavior

The goal of the logistic loss function is:

- Create a large loss if the target = 1 and the prediction = ~0
- Create a small loss if the target = 1 and the prediction = ~1
- Create a large loss if the target = 0 and the prediction = ~1
- Create a small loss if the target = 0 and the prediction = ~0

This is what that behavior looks like:

If you want a full example that shows the graphic, take this code:

import math import matplotlib.pyplot as plt def log_loss(act, target): """ target == 0 -> -math.log(1 - act) target == 1 -> -math.log(act) """ return -target * math.log(act) - (1 - target) * math.log(1 - act) fig, ax = plt.subplots() predictions = [r / 100 for r in range(1, 100)] # -> [.01, 0.02 ... 0.99] losses_for_target_one = [log_loss(p, 1) for p in predictions] losses_for_target_zero = [log_loss(p, 0) for p in predictions] ax.plot(predictions, losses_for_target_one) ax.plot(predictions, losses_for_target_zero) ax.set_xlabel("Activation") ax.set_ylabel("Loss") plt.grid(True) plt.show()

Written by

**Loek van den Ouweland**on 2021-11-30. Questions regarding this artice? You can send them to the address below.