View source for Binary cross-entropy loss

The binary cross-entropy loss is given by:
:<math>
L = - \frac{1}{m} \sum_{i=1}^{m} \left[ y_i \cdot \log{ (\hat{y_i}) } + (1-y_i) \cdot  \log{ (1-\hat{y_i}) } \right]
</math>
for <math>m</math> training examples (indexed by <math>i</math>) where <math>y_i</math> is the class label (0 or 1) and <math>\hat{y_i}</math> is the prediction for that example (i.e. the predicted probability that it is a positive example). Thus <math>1-\hat{y_i}</math> is the probability that it is a negative example.


====True Positive====
:<math>
\left[ 1 \cdot 0 + (0) \cdot  -\infty \right] \approx 0
</math>
====False Negative====
:<math>
\left[ 1 \cdot -\infty + (0) \cdot  0 \right] \approx -\infty
</math>
====False Positive====
:<math>
\left[ 0 \cdot 0 + (1) \cdot  -\infty \right] \approx -\infty
</math>
====True Negative====
:<math>
\left[ 0 \cdot -\infty + (1) \cdot  0 \right] \approx 0
</math>