Binary cross-entropy loss

The binary cross-entropy loss is given by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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] }

for $m$ training examples (indexed by $i$) where $y_{i}$ is the class label (0 or 1) and ${\hat {y_{i}}}$ is the prediction for that example (i.e. the predicted probability that it is a positive example). Thus Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 1-{\hat {y_{i}}}} is the probability that it is a negative example.