AUC as the Mann-Whitney rank statistic

Compute ROC AUC from ranks, with ties averaged

The area under the ROC curve equals the probability that a randomly chosen positive example scores higher than a randomly chosen negative one, with ties counting one half. That is the Mann-Whitney U statistic divided by the number of pairs. If R_pos is the sum of the positives' ranks (ascending, ties averaged), then

AUC = (R_pos - n_pos (n_pos + 1) / 2) / (n_pos * n_neg).

Implement auc_rank(scores, labels) with labels in {0, 1}. Return the AUC as a float.

Constraints

• scores and labels are 1-D arrays of equal length.
• labels holds only 0 and 1. Otherwise raise ValueError.
• Both classes must be present. Otherwise raise ValueError.
• Do not modify the inputs.

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