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

arXiv: https://arxiv.org/abs/2608.10893 · HTML: https://mlsanity.com/paper/2608.10893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 64 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Mitigating LLM Hallucinations via Conformal Abstention](https://mlsanity.com/paper/2405.01563/) (2024)
- [Model-free selective inference under covariate shift via weighted conformal p-values](https://mlsanity.com/paper/2307.09291/) (2023)
- [Conformal Selective Prediction with General Risk Control](https://mlsanity.com/paper/2603.24704/) (2026)
- [Selective Conformal Risk Control](https://mlsanity.com/paper/2512.12844/) (2025)
- [LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems](https://mlsanity.com/paper/2512.01556/) (2025)
- [RACER: Risk-Aware Calibrated Efficient Routing for Large Language Models](https://mlsanity.com/paper/2603.06616/) (2026)
- [Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation](https://mlsanity.com/paper/2310.16638/) (2023)
- [Non-exchangeable Conformal Prediction with Optimal Transport: Tackling Distribution Shifts with Unlabeled Data](https://mlsanity.com/paper/2507.10425/) (2025)
- [A Joint Finite-Sample Certificate for Adaptive Selective Conformal Risk Control](https://mlsanity.com/paper/2606.08517/) (2026)
- [Weight Clipping for Robust Conformal Inference under Unbounded Covariate Shifts](https://mlsanity.com/paper/2605.02072/) (2026)
- [BalanceRAG: Joint Risk Calibration for Cascaded Retrieval-Augmented Generation](https://mlsanity.com/paper/2605.20084/) (2026)
- [Reliable Abstention under Adversarial Injections: Tight Lower Bounds and New Upper Bounds](https://mlsanity.com/paper/2602.20111/) (2026)
- [Conformal Risk Control under Non-Monotone Losses: Theory and Finite-Sample Guarantees](https://mlsanity.com/paper/2604.01502/) (2026)
- [Inference-Time Conformal Reasoning with Valid Factuality Control for Large Language Models](https://mlsanity.com/paper/2606.08831/) (2026)
- [Conformal Prediction Adaptive to Unknown Subpopulation Shifts](https://mlsanity.com/paper/2506.05583/) (2025)
- [Multi-Distribution Robust Conformal Prediction](https://mlsanity.com/paper/2601.02998/) (2026)
- [KMM-CP: Practical Conformal Prediction under Covariate Shift via Selective Kernel Mean Matching](https://mlsanity.com/paper/2603.26415/) (2026)
- [Chance-Constrained Inference for Hallucination Risk Control in Large Language Models](https://mlsanity.com/paper/2602.01637/) (2026)
- [Multicalibration Boosting: Theory, Convergence, and Transferability](https://mlsanity.com/paper/2605.24364/) (2026)

## Abstract (arXiv)

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→0, 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.