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.

翻译：现实世界中的学习任务常因协变量偏移及噪声或不一致标签而面临不确定性。然而，现有的鲁棒学习方法将这两种影响合并为单一分布不确定性集。本文提出一种新颖的结构化置信学习框架，明确分离这两种不确定性来源。具体而言，我们推导了结构化置信集在总变差直径上的几何界，并证明该量如何分解为协变量偏移与期望标签分歧的贡献。该分解揭示了一种门控效应：协变量调节标签分歧对联合不确定性的贡献程度，使得看似良性的协变量偏移可能显著增加有效不确定性。我们还在固定协变量机制下建立了有限样本集中界，并证明该量可被高效估计。最后，我们证明在这些结构化置信集上的鲁棒优化可简化为一个易处理的离散极小极大问题，从而避免临时设定的鲁棒性参数。总体而言，我们的方法为协变量与标签机制双重模糊下的鲁棒学习提供了原则性且实用的理论基础。