Certified score envelopes for exact candidate elimination

Determine whether certified score envelopes can convert posterior ranking into exact candidate elimination while retaining the same moment-based geometry.

Background

The paper develops Hankel–Christoffel–Nevai scores that estimate posterior relevance from likelihood-weighted moment geometry. These scores can rank or approximately screen candidates, but discarding candidates based solely on approximate scores may alter the target posterior. The paper separately shows that learned scores can safely reorder exact stochastic likelihood blocks without changing the posterior law.

The unresolved question is whether one can construct certified upper and lower envelopes around such scores that are sufficiently rigorous to support exact elimination of candidates, while preserving the moment-based posterior-relevance framework. Such a result would combine the computational savings of screening with the exactness guarantees of posterior computation.

References

A further question is whether certified score envelopes can convert posterior ranking into exact candidate elimination while retaining the same moment-based geometry.

— Hankel-Christoffel-Nevai Screening of Posterior Relevance in Bayesian Inverse Problems  (2609.20711 - Deng et al., 17 Sep 2026) in Section Conclusion

The certificate limit for $K>2$ is left open.

— How Many Labels Does Model Choice Need? Certificates and Budgets for Selective Prediction  (2609.18622 - Kuboyama, 16 Sep 2026) in Section 6, subsection “Finite-pool simulations and correlated orders,” paragraph “Independent orders”