AI RESEARCH
The Minimax Rate of Second-Order Calibration
arXiv CS.LG
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ArXi:2605.07808v1 Announce Type: new We characterize the minimax rate of estimating the second-order calibration error for binary classification, which quantifies whether a higher-order predictor's epistemic-uncertainty estimate matches the conditional variance of the label probability on its level sets. Our key observation is that the sech perturbation kernel, previously used only to enforce smoothness of calibration functions, in fact makes them analytic in a strip of half-width $h\pi/2