Calibration Count Reuse: Validity Does Not Determine Efficiency

Abstract:Calibration count reuse raises separate validity and efficiency questions. We give a validity criterion for general count-dependent nonconformity scores: transferring one count from another class to the scored class must not improve its conformity. A leave-self-out full conformal reference proves the criterion without requiring normalization or preservation of same-class score order. For a common separable transformation, universal exchangeable validity is equivalent to being nondecreasing in the count, provided $K\alpha \geq 1$; normalized multiplicative weights obey the complementary nonincreasing condition. Additive penalties are covered under the stated information restrictions. Efficiency has no parallel ordering: two iid constructions make the same valid rule improve or worsen expected size at unchanged coverage. An expanded 55-rule study finds no resolved advantage from selected live-count rules over uniform weights. Image studies identify undercoverage under iid resampling, including at numerical convergence. Separately, execution of the released Conf-OT pipeline on its DTD and Aircraft benchmark subsets produces near-nominal median coverage under fixed stratified counts. The native results are reported separately from the iid analyses, without treating a benchmark observation as a universal guarantee. The findings separate validity, classifier confidence, numerical convergence, and population-specific efficiency.

Methodology (stat.ME); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG)

arXiv:2609.25138 [stat.ME]

(or arXiv:2609.25138v1 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2609.25138 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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