Anytime-Valid Confirmation of Label-Shift Corrections

Abstract:In small-batch scientific deployments, labeled target outcomes may be too scarce for reliable shift estimation even when unlabeled target inputs are available. We address the complementary setting where the practitioner has a pre-specified label-shift correction from domain knowledge and asks whether incoming labeled outcomes support it. We show that the per-observation likelihood ratio between a label-shift-corrected predictive and the source predictive is a conditional e-value, so its running product is a nonnegative martingale and Ville's inequality yields an anytime-valid confirmation rule. The log martingale equals the cumulative negative log-predictive density (NLPD) gap between the source and the corrected predictive, converting routine model monitoring into a formal sequential test. Rejection means the incoming data support the posited correction relative to the source predictive, but it is not a precise estimate of the degree of shift. Closed forms are available for GP sources with Gaussian label-shift ratios. GP regression simulations validate Type I control, finite-sample power, miscalibration sensitivity, and the small-batch advantage of a reliable prior over label-based re-estimation.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2606.14028 [stat.ML]

(or arXiv:2606.14028v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2606.14028 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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