We consider the problem of distribution-free conformal prediction and the criterion of group conditional validity. This criterion is motivated by many practical scenarios including hidden stratification and group fairness. Existing methods achieve such guarantees under either restrictive grouping structure or distributional assumptions, or they are overly-conservative under heteroskedastic noise. We propose a simple reduction to the problem of achieving validity guarantees for individual populations by leveraging algorithms for a problem called multi-group learning. This allows us to port theoretical guarantees from multi-group learning to obtain obtain sample complexity guarantees for conformal prediction. We also provide a new algorithm for multi-group learning for groups with hierarchical structure. Using this algorithm in our reduction leads to improved sample complexity guarantees with a simpler predictor structure.

翻译：本文研究无分布假设下的共形预测问题及组条件有效性准则。该准则受许多实际场景（包括隐藏分层和组公平性）启发而提出。现有方法要么受限于严格的组结构或分布假设，要么在异方差噪声下过于保守。我们提出一种简洁方法，通过利用名为多组学习的问题算法，将问题转化为为个体群体提供有效性保证。这使得我们能够将多组学习的理论保证迁移至共形预测，从而获得样本复杂度保证。我们还针对具有层级结构的组提出了一种新的多组学习算法。将该算法应用于我们的转化方法后，能以更简洁的预测器结构获得更优的样本复杂度保证。