Platt Scaling for Classifier Scores

SVMs and boosted trees output scores, not probabilities. Platt scaling fits a 1-D logistic regression on held-out scores: $P(y = 1 \mid s) = \sigma(a s + b)$.

Implement:

• fit_platt(scores, labels, iters=50): find a and b by Newton's method on the log loss, starting from a = 0 and b = log((pos + 1) / (neg + 1)). Return (a, b).
• platt_predict(a, b, scores)
• log_loss(probs, labels, eps=1e-12): the mean binary cross-entropy, clipping probabilities to [eps, 1 - eps]