Multivariate Standardized Residuals for Conformal Prediction

arXiv:2507.20941v3 Announce Type: replace
Abstract: While split conformal prediction guarantees marginal coverage, approaching the stronger property of conditional coverage is essential for reliable uncertainty quantification. Naive conformal scores, however, suffer from poor conditional coverage in heteroskedastic settings. In univariate regression, this is commonly addressed by normalizing nonconformity scores using estimated local score variance. In this work, we propose a natural extension of this normalization to the multivariate setting, effectively whitening the residuals to decouple output correlations and standardize local variance. We demonstrate that using the Mahalanobis distance induced by a learned local covariance as a nonconformity score provides a closed-form, computationally efficient mechanism for capturing inter-output correlations and heteroskedasticity, avoiding the expensive sampling required by previous methods based on cumulative distribution functions. This structure unlocks several practical extensions, including the handling of missing output values, the refinement of conformal sets when partial information is revealed, and the construction of valid conformal sets for transformations of the output. Finally, we provide extensive empirical evidence on both synthetic and real-world datasets showing that our approach yields conformal sets that significantly improve upon the conditional coverage of existing multivariate baselines.