Conformal prediction, and split conformal prediction as a specific implementation, offer a distribution-free approach to estimating prediction intervals with statistical guarantees. Recent work has shown that split conformal prediction can produce state-of-the-art prediction intervals when focusing on marginal coverage, i.e. on a calibration dataset the method produces on average prediction intervals that contain the ground truth with a predefined coverage level. However, such intervals are often not adaptive, which can be problematic for regression problems with heteroskedastic noise. This paper tries to shed new light on how prediction intervals can be constructed, using methods such as normalized and Mondrian conformal prediction, in such a way that they adapt to the heteroskedasticity of the underlying process. Theoretical and experimental results are presented in which these methods are compared in a systematic way. In particular, it is shown how the conditional validity of a chosen conformal predictor can be related to (implicit) assumptions about the data-generating distribution.

翻译：共形预测及其具体实现——分裂共形预测，提供了一种无分布假设的方法，用于估计具有统计保证的预测区间。近期研究表明，当聚焦于边际覆盖时（即在校准数据集上，该方法平均产生的预测区间以预定义覆盖水平包含真实值），分裂共形预测能够生成最先进的预测区间。然而，此类区间往往缺乏自适应性，这可能对存在异方差噪声的回归问题造成困扰。本文旨在通过归一化共形预测和蒙德里安共形预测等方法，揭示如何构建能够自适应底层过程异方差性的预测区间。我们系统性地比较了这些方法，并给出了理论及实验结果。特别地，我们展示了所选共形预测器的条件有效性如何与关于数据生成分布的（隐式）假设相关联。