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

• URL: http://arxiv.org/abs/2608.10893v1
• Date: Tue, 11 Aug 2026 13:10:55 GMT
• Title: Certify or Refuse: A Cross-Model Map for Selective Risk Control with Coverage Floors under Covariate Shift
• Abstract summary: We show that selective predictors attain whatever coverage they attain by imposing an automation floor.<n> certification acquires a feasibility frontier and a two-resource complexity map, additive up to constants.<n>The rates are local, needing a regular frontier margin, slack below the local-regime threshold, and lattice conditions.
• Score: 4.621071191322703
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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