F-beta score

The problem, from first principles

F1 weighs precision and recall equally. Sometimes that is wrong: a cancer screen must not miss cases (recall matters more), while a fraud alert that blocks good customers must not be noisy (precision matters more). F-beta lets you choose. beta > 1 leans toward recall and beta < 1 leans toward precision. beta = 1 gives F1.

Implement fbeta_score(y_true, y_pred, beta=1.0, positive=1) for binary labels.

• Precision P = TP / (TP + FP), or 0.0 when TP + FP is zero.
• Recall R = TP / (TP + FN), or 0.0 when TP + FN is zero.
• Return (1 + beta²) · P · R / (beta² · P + R), or 0.0 when the denominator is zero.

Constraints

• beta must be greater than zero, otherwise raise ValueError.
• Inputs must have the same length.

Hints

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