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Binary Cross-Entropy Loss

Compute the binary cross-entropy loss (log loss) for a set of predictions.

Given true labels $y_i \in \{0, 1\}$ and predicted probabilities $\hat{y}_i \in (0, 1)$ :

$BCE = -\frac{1}{n}\sum_{i=1}^{n}[y_i \log(\hat{y}_i) + (1 - y_i)\log(1 - \hat{y}_i)]$

To avoid $\log(0)$ , clip predictions to the range $[\epsilon, 1-\epsilon]$ where $\epsilon = 10^{-7}$ .

Return the loss rounded to 4 decimal places.

Input:

y_true = [1, 0, 1]
y_pred = [0.9, 0.1, 0.8]

Output:

0.1446

Reasoning:

First, we clip the predicted probabilities to the range $[\epsilon, 1-\epsilon]$ where $\epsilon = 10^{-7}$ : $y_{pred} = [0.9, 0.1, 0.8]$ remains the same since all values are within the range.
Then, we calculate the binary cross-entropy loss for each sample:
- For $y_i = 1$ and $\hat{y}_i = 0.9$ , the loss is $-\log(0.9)$
- For $y_i = 0$ and $\hat{y}_i = 0.1$ , the loss is $-\log(1-0.1) = -\log(0.9)$
- For $y_i = 1$ and $\hat{y}_i = 0.8$ , the loss is $-\log(0.8)$
Next, we calculate the total loss by summing the individual losses and dividing by the number of samples $n=3$ : $BCE = -\frac{1}{3}[\log(0.9) + \log(0.9) + \log(0.8)]$
The final output is the loss rounded to 4 decimal places: $BCE \approx 0.1446$

Editor

Python 3.13.1

0/0

Run code to see test results.

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