How Much Can Reliability Drift Under a Fixed Confidence Distribution?

Wenhao Liang, Lin Yue, Wei Emma Zhang, Mingyu Guo, Olaf Maennel +1

A classifier's conditional accuracy can change while its confidence distribution stays exactly the same. We study the worst-case movement of the reliability relation under covariate shifts that preserve the distribution of the confidence score, constraining the reweighting within each confidence level by a $χ^2$ budget; the resulting worst case, as a function of the budget, is a fragility profile. On an interval of budgets that can be computed from the source distribution, the profile equals exactly the square root of the budget times the within-level variance of the correctness propensity -- the grouping-loss term of calibration-refinement decompositions. Beyond this interval the profile is governed by the tails of the propensity law, and the entire upward profile determines the centred within-level law; consequently, calibration residual and grouping variance do not determine fragility in general, though they do when labels and predictions are deterministic. Since the propensity is not observed, we restrict reweightings to a learned finite readout within confidence bins, bound the part the restriction misses by the grouping variance remaining inside readout cells, estimate the…