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Conformal prediction is a statistical tool for producing prediction regionsfor machine learning models that are valid with high probability. A keycomponent of conformal prediction algorithms is a non-conformity score functionthat quantifies how different a model's prediction is from the unknown groundtruth value. Essentially, these functions determine the shape and the size ofthe conformal prediction regions. However, little work has gone into findingnon-conformity score functions that produce prediction regions that aremulti-modal and practical, i.e., that can efficiently be used in engineeringapplications. We propose a method that optimizes parameterized shape templatefunctions over calibration data, which results in non-conformity scorefunctions that produce prediction regions with minimum volume. Our approachresults in prediction regions that are multi-modal, so they can properlycapture residuals of distributions that have multiple modes, and practical, soeach region is convex and can be easily incorporated into downstream tasks,such as a motion planner using conformal prediction regions. Our method appliesto general supervised learning tasks, while we illustrate its use intime-series prediction. We provide a toolbox and present illustrative casestudies of F16 fighter jets and autonomous vehicles, showing an up to $68\%$reduction in prediction region area.

Multi-Modal Conformal Prediction Regions by Optimizing Convex Shape Templates