Log loss (cross-entropy)

The problem, from first principles

A classifier that outputs probabilities should be scored on those probabilities, not only on the hard label. Log loss punishes confident wrong answers heavily: predicting 0.99 for a true negative costs far more than predicting 0.6. It is the average negative log-likelihood of the true labels under the predicted probabilities.

Implement log_loss(y_true, y_prob, eps=1e-15) for binary labels, where y_prob is the predicted probability of class 1.

• Clip probabilities to [eps, 1 - eps] so log(0) never occurs.
• Return −mean(y log p + (1 − y) log(1 − p)).

Constraints

• y_true values must be 0 or 1, and y_prob values must lie in [0, 1]. Otherwise raise ValueError.
• Inputs must have the same length and be non-empty.

Hints

Open one at a time. Each gives away a little more than the last.