Conformal prediction (CP) offers distribution-free marginal coverage guarantees under an exchangeability assumption, but these guarantees can fail if the data distribution shifts. We analyze the use of pseudo-calibration as a tool to counter this performance loss under a bounded label-conditional covariate shift model. Using tools from domain adaptation, we derive a lower bound on target coverage in terms of the source-domain loss of the classifier and a Wasserstein measure of the shift. Using this result, we provide a method to design pseudo-calibrated sets that inflate the conformal threshold by a slack parameter to keep target coverage above a prescribed level. Finally, we propose a source-tuned pseudo-calibration algorithm that interpolates between hard pseudo-labels and randomized labels as a function of classifier uncertainty. Numerical experiments show that our bounds qualitatively track pseudo-calibration behavior and that the source-tuned scheme mitigates coverage degradation under distribution shift while maintaining nontrivial prediction set sizes.

翻译：共形预测（CP）在可交换性假设下提供与分布无关的边际覆盖保证，但当数据分布发生偏移时，这些保证可能失效。本文分析了在有限标签条件协变量偏移模型下，使用伪校准作为应对此类性能损失的工具。借助域自适应理论工具，我们推导出目标域覆盖率的显式下界，该下界由分类器的源域损失与偏移的Wasserstein度量共同表征。基于此结果，我们提出一种设计伪校准集的方法，通过引入松弛参数扩展共形阈值，使目标覆盖率维持在预设水平之上。最后，我们提出一种源域调谐的伪校准算法，该算法根据分类器的不确定性，在硬伪标签与随机化标签之间进行自适应插值。数值实验表明，所得理论边界能定性追踪伪校准的行为特征，且源域调谐方案在保持非平凡预测集规模的同时，有效缓解了分布偏移下的覆盖率衰减。