Finite-sample target-risk guarantees for OT-based reweighting

Establish a finite-sample guarantee on the target risk of classifiers trained with POTER's data-dependent optimal-transport weights under label shift.

Background

The paper proves the classwise decomposition of the class-conditioned optimal-transport problem and derives the unique KL-regularized reweighting solution for fixed dual potentials. These results characterize the weight construction but do not analyze the statistical performance of a classifier trained with those weights.

The unresolved analysis concerns relating the population reweighted objective to target risk under label shift, controlling estimation error in the optimal-transport dual potentials and resulting sample weights, and establishing generalization for weighted empirical risk minimization with data-dependent weights. Such a guarantee would connect POTER's finite-sample construction to target-distribution performance.

References

These results do not provide a finite-sample guarantee on the target risk of a classifier trained using the resulting weights. Under label shift, where class proportions change while class-conditional distributions remain fixed, establishing such a guarantee would additionally require relating the population reweighted objective to the target risk, controlling estimation error in the OT potentials and sample weights, and analyzing the generalization of weighted ERM with these data-dependent weights. We leave such an analysis to future work.

— Optimal Transport Reweighting for Robust Learning under Spurious Correlations and Label Noise  (2610.01028 - Jo et al., 1 Oct 2026) in Appendix B, paragraph “Scope of the theoretical results”