Average precision
The problem, from first principles
A precision-recall curve needs a summary number for comparing models. Average precision (AP) is the area under that curve, computed as a step function: each time recall increases, add the precision at that point, weighted by how much recall increased. It rewards putting positives near the top of the ranking, and it is far more informative than ROC AUC when positives are rare.
Implement average_precision(y_true, scores) for binary labels, where higher score means more likely positive (label 1).
- Sort rows by score, descending. Tied scores form one threshold: evaluate only after the last row of each tie group.
- At each threshold, compute precision = TP / (TP + FP) and recall = TP / total positives.
- AP = Σ (recall_k − recall_{k−1}) · precision_k, with recall_0 = 0.
Constraints
- Inputs must have the same length, otherwise raise
ValueError. - If there are no positive labels, raise
ValueError.
Hints
Open one at a time. Each gives away a little more than the last.
Hint 1
np.argsort(-scores, kind="stable") orders the rows, and np.cumsum over the sorted labels gives TP at every row.
Hint 2
Keep only the positions where the sorted score changes, plus the last position. np.diff(sorted_scores) != 0 finds the changes.
Keywords
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