Binary Cross-Entropy Loss
Beginner
The problem, from first principles
Classification needs to distinguish uncertainty from confidently choosing the wrong class. A loss should therefore charge a much larger cost when a predicted probability disagrees with the true binary label. The logarithm does that, but only if its input is kept away from zero.
From theory to code
Implement bce_loss(p, y) as a batch mean. Theory gives the two label cases; clip probabilities before either logarithm and return a Python float.
Constraints
pand binaryyhave matching(n_samples,)shapes.- Clip
pto[1e-12, 1 - 1e-12]before logs. - Average one loss value per sample and return a plain
float. - Saturated
0.0and1.0inputs must produce a finite loss. - Use vectorized NumPy operations only.
Hints
Open one at a time. Each gives away a little more than the last.
Hint 1
Each label selects one of two complementary probability terms.
Hint 2
Clip once, then form both log(p) and log(1 - p) before taking the negative mean.
Keywords
classical-mlclassificationloss-functions
Python
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