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.

通过优化参数化形状模板函数的方法，我们提出了一种能够产生多模态预测区域的非一致性评分函数，使得每个区域是凸的、易于在后续任务中引入的实用预测区域，主要适用于监督学习任务，本研究以时间序列预测为例，可应用于F16战斗机和自动驾驶车辆等案例研究，预测区域面积可减少高达68%。

通过优化凸形模板生成多模态适应性预测区域