Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift

2026-08-11

AI Summary

This work addresses selective risk control under covariate shift by ensuring that a predictor covers at least a β-fraction of target-domain samples while maintaining an error rate no greater than α. To achieve this coverage-constrained guarantee, the authors propose the Floor Certification Map, which decouples dependencies between labeled source data and unlabeled target data through local acceptance region functional analysis, grid-based conditional assumptions, and a preregistered stratified shift model. Theoretically, they establish a cross-model feasibility frontier and a dual-resource complexity profile, proving that uniform estimation over all classes is impossible and characterizing the local complexity structure of the risk–coverage trade-off via matching upper and lower bounds. Algorithmically, they develop an implementable oracle-weight estimation procedure. Experiments demonstrate that the preregistered approach yields honest rejections in SQuAD→NewsQA transfer, achieves zero violations in 1024-unit audits, and exhibits a log-log slope of −2.002.

Abstract

Certified selective predictors attain whatever coverage they attain; operators impose an automation floor: answer at least a $β$-fraction of shifted target traffic with at most an $α$-fraction of answers wrong. Under bounded-ratio covariate shift we prove the Floor Certification Map: once that floor must be certified alongside the selection-conditioned risk $α$, certification acquires a feasibility frontier and a two-resource complexity map, additive up to constants: risk in labeled source, the floor in unlabeled target samples. The rates are local, needing a regular frontier margin, slack below the local-regime threshold, and lattice conditions: pre-registered with a lattice margin for the upper bounds, compatible per-slack for the lower. The displayed split is the operational route; oracle weights also allow a labeled-source floor estimate. Three model-tagged results: a lower bound (Model-B), a matching oracle-weight upper bound (Model-A), and an implementable upper bound (Model-B') valid under a pre-registered exact stratified-shift model with nuisance cost priced explicitly. The match is across these models rather than a single-model minimax theorem, and necessarily so: over the full bounded-ratio class no unknown-weight procedure matches at any sample size (Model-B is inconsistent, witnessed at $α=β=1/2$). The nuisance's necessity is only partially settled. Complexity tracks a localized accepted-region functional, not global effective sample size (ESS), on both sides, though a fixed-ESS separation theorem is left open; both lower-bound axes vanish as $β\to0$, so the floor creates the map. Empirically, the registered bite family diverges with log-log slope $-2.002$ within its pre-registered band; a 1,024-cell audit records 0 violations where the formal certificates fire; and a single-corpus SQuAD-to-NewsQA feasibility audit returns honest refusal.

Problem

• selective prediction
• covariate shift
• coverage floor
• risk control
• certification

Innovation

• selective prediction
• covariate shift
• coverage floor
• certification map
• localized complexity