Structured Credal Learning

TL;DR

This paper introduces a structured credal learning framework that explicitly separates covariate shift and label noise, providing geometric bounds, concentration results, and a tractable optimization approach for robust learning.

Contribution

It presents a novel framework that decomposes uncertainty into covariate and label components, with geometric bounds and an efficient optimization method for robust learning.

Findings

Decomposition of total variation diameter into covariate and label contributions.

Finite-sample concentration bounds for the structured credal sets.

Reduction of robust optimization to a tractable min-max problem.

Abstract

Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we introduce a novel structured credal learning framework that explicitly separates these two sources. Specifically, we derive geometric bounds on the total variation diameter of structured credal sets and demonstrate how this quantity decomposes into contributions from covariate shift and expected label disagreement. This decomposition reveals a gating effect: covariate modulates how much label disagreement contributes to the joint uncertainty, such that seemingly benign covariate shifts can substantially increase the effective uncertainty. We also establish finite-sample concentration bounds in a fixed covariate regime and demonstrate that this quantity can be efficiently estimated. Lastly, we show that robust optimization over these structured credal sets reduces to a tractable discrete min-max problem, avoiding ad-hoc robustness parameters. Overall, our approach provides a principled and practical foundation for robust learning under combined covariate and label mechanism ambiguity.