aiqbench analysis
This paper gives theory and procedures for certifying that a probabilistic predictor is miscalibrated when no ground-truth labels are available. It derives sharp label-free lower bounds, shows that the bounds can be discontinuous and that Lipschitz-constrained stakes yield stable ones, and offers online and anytime-valid estimators. The main caveat is that a positive certificate proves only a lower bound on miscalibration, while zero means only "not refuted," so practitioners should read it as a diagnostic rather than a clean guarantee.
Sharp and Stable Label-Free Calibration Certificates from Logical Coherence
arXiv:2610.21567v1 Announce Type: new Abstract: Query-conditioned probabilistic predictors answer logically related questions one at a time, and labels to check their calibration are often missing. For each restriction on what a bettor's stakes may use, a minimax theorem identifies, for finitely supported laws of the answers, the sharp label-free lower bound on the corresponding calibration residual. On bundles of different events its mean, marginal and joint stages can separate strictly, and a bundle's bound cannot be attributed to one question without assumptions on the others. The sharp marginal bound is discontinuous in the answers, and no label-free lower bound continuous in the Wasserstein distance stays within a constant factor of it. Lipschitz stakes give a stable bound, sharp for a smooth calibration residual and, for every positive Lipschitz constant, positive exactly when the sharp marginal bound is. On i.i.d. streams, projected online gradient ascent at fixed nodes gives fixed-horizon certificates whose shortfall is bounded by grid, learning and statistical terms, and predictable betting gives anytime-valid ones. In a preregistered study of four predictors on two data sets, all seven confirmatory certificates were positive (the eighth pair did not pass the pilot). A certificate shows only that calibration is at least this bad; zero means "not refuted".
Abstract:Query-conditioned probabilistic predictors answer logically related questions one at a time, and labels to check their calibration are often missing. For each restriction on what a bettor's stakes may use, a minimax theorem identifies, for finitely supported laws of the answers, the sharp label-free lower bound on the corresponding calibration residual. On bundles of different events its mean, marginal and joint stages can separate strictly, and a bundle's bound cannot be attributed to one question without assumptions on the others. The sharp marginal bound is discontinuous in the answers, and no label-free lower bound continuous in the Wasserstein distance stays within a constant factor of it. Lipschitz stakes give a stable bound, sharp for a smooth calibration residual and, for every positive Lipschitz constant, positive exactly when the sharp marginal bound is. On i.i.d. streams, projected online gradient ascent at fixed nodes gives fixed-horizon certificates whose shortfall is bounded by grid, learning and statistical terms, and predictable betting gives anytime-valid ones. In a preregistered study of four predictors on two data sets, all seven confirmatory certificates were positive (the eighth pair did not pass the pilot). A certificate shows only that calibration is at least this bad; zero means "not refuted".
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2610.21567 [cs.LG]
(or arXiv:2610.21567v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.21567 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 298 words
