Conformal prediction is a statistical tool for producing prediction regions for machine learning models that are valid with high probability. A key component of conformal prediction algorithms is a non-conformity score function that quantifies how different a model's prediction is from the unknown ground truth value. Essentially, these functions determine the shape and the size of the conformal prediction regions. However, little work has gone into finding non-conformity score functions that produce prediction regions that are multi-modal and practical, i.e., that can efficiently be used in engineering applications. We propose a method that optimizes parameterized shape template functions over calibration data, which results in non-conformity score functions that produce prediction regions with minimum volume. Our approach results in prediction regions that are multi-modal, so they can properly capture residuals of distributions that have multiple modes, and practical, so each region is convex and can be easily incorporated into downstream tasks, such as a motion planner using conformal prediction regions. Our method applies to general supervised learning tasks, while we illustrate its use in time-series prediction. We provide a toolbox and present illustrative case studies of F16 fighter jets and autonomous vehicles, showing an up to $68\%$ reduction in prediction region area.

翻译：共形预测是一种统计工具，用于生成机器学习模型的高置信度预测区域。共形预测算法的核心是非一致性评分函数，该函数量化模型预测与未知真实值之间的差异。本质上，这些函数决定了共形预测区域的形状和大小。然而，目前鲜有研究致力于设计能够产生多模态且实用的预测区域（即能高效应用于工程领域）的非一致性评分函数。我们提出了一种方法，通过在校准数据上优化参数化的形状模板函数，得到最小化预测区域体积的非一致性评分函数。该方法生成的预测区域具有多模态特性，可准确捕捉带有多个峰值的残差分布；同时兼具实用性，每个区域均为凸集，便于集成到下游任务中（例如基于共形预测区域的运动规划器）。本方法适用于通用的监督学习任务，并以时间序列预测为例进行说明。我们提供了工具包，并通过F16战斗机和自动驾驶汽车的案例研究展示了其效果，预测区域面积最多可减少68%。