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 adaptive prediction intervals can be constructed using methods such as normalized and Mondrian conformal prediction. We present theoretical and experimental results in which these methods are investigated in a systematic way.

翻译：保形预测，以及作为其具体实现的分裂保形预测，提供了一种无需分布假设的方法，用于估计具有统计保证的预测区间。近期研究表明，在关注边际覆盖率时，即在校准数据集上该方法平均生成的预测区间能以预定义覆盖率包含真实值，分裂保形预测可产生最先进的预测区间。然而，此类区间通常不具有自适应性，这在存在异方差噪声的回归问题中可能带来问题。本文试图阐明如何利用归一化保形预测和蒙德里安保形预测等方法构建自适应预测区间。我们提出系统研究这些方法的理论及实验结果分析。