Interpretable Multivariate Conformal Prediction with Balanced and Jointly Calibrated Rectangular Envelopes

Nabil Alami, Rafael Izbicki, Souhaib Ben Taieb

Keywords: Conformal Prediction, Multivariate regression, Calibration

TL;DR: We propose an interpretable construction of multi-output conformal prediction set as a cartesian product of low dimensional regions with a novel nonconformity score.

Abstract: Multi-output conformal prediction methods often produce flexible but hard-to-interpret prediction sets, while alternative approaches yield hyperrectangular regions that can be overly conservative. We propose a framework that bridges these two paradigms by constructing prediction sets as Cartesian products of regions defined on low-dimensional output partitions. To ensure joint coverage, we introduce three calibration strategies and clarify their connection to the notion of asymptotic balance, which seeks to equalize miscoverage across partitions asymptotically. Motivated by interpretability in high-dimensional output settings, we further propose a novel nonconformity score that generates efficient hyperrectangular sets. Experiments on real-world datasets demonstrate that our method improves efficiency over existing baselines while preserving interpretability and achieving asymptotic balance.

Submission Number: 36