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：我们考虑无分布假设的共形预测问题及群体条件有效性准则。该准则的提出源于诸多实际场景，包括隐藏分层和群体公平性。现有方法或依赖严格的群体结构假设与分布假设，或在异方差噪声下过于保守。我们提出了一种简洁的归约方法，通过利用名为"多组学习"问题的算法，实现对个体群体的有效性保证。该策略使我们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。此外，我们针对具有层级结构的群体提出了一种新的多组学习算法。在归约过程中使用该算法，能以更简洁的预测器结构获得更优的样本复杂度保证。