How the harm test works

Why a separate test

A distribution can change without becoming worse. A generic shift test should detect both changes, but monitoring often asks a narrower question: did the target move toward outcomes that matter? The answer depends on the score being monitored and on which direction is harmful.

Without loss of generality, assume that a higher score means more harmful or riskier outcomes. The worse parameter handles scores whose harmful direction is lower instead. Choose that direction from the meaning of the score, not from the p-value.

Tail-focused separation

For an oriented score S and threshold t, define

\[ \operatorname{FPR}(t) = P(S > t \mid \text{source}), \qquad \operatorname{TPR}(t) = P(S > t \mid \text{target}). \]

The ordinary shift statistic is ROC AUC: it weights thresholds uniformly. The harm statistic gives more weight to thresholds that the source rarely exceeds:

\[ \operatorname{AUC} = \int \operatorname{TPR}(t)\,d\operatorname{FPR}(t), \qquad T = \int \operatorname{TPR}(t)\,[1-\operatorname{FPR}(t)]^2\, d\operatorname{FPR}(t). \]

Here, T is the weighted AUC: the test statistic used by test_harm. The statistic measures directional separation.

Since 1 - FPR(t) is the source probability below the threshold, this emphasizes target observations entering the source's unusual upper tail. AUC treats all thresholds equally. The harm statistic puts more emphasis on target observations beyond the source's usual range. This makes it more sensitive to target observations entering regions rarely observed in source than to movement among values commonly observed in benign source samples.

How to choose the test

• Use test_shift when any distributional difference matters.
• Use test_harm when you can declare the harmful direction before looking at the result.

Both tests compare the same source and target scores by permutation. The harmful-shift test changes the threshold weighting and uses a one-sided alternative.

See Shift testing for the function signatures and Get started for a complete score and test workflow.

Reference

Kamulete, V. M. (2022). Test for non-negligible adverse shifts (D-SOS). Proceedings of UAI, PMLR 180:959-968. PMLR and arXiv:2107.02990.