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Naive conformal scores, however, suffer from poor conditional coverage in heteroskedastic settings. In univariate regression, this is commonly addressed by normalizing non-conformity scores using an 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. Furthermore, we derive a sufficient condition characterizing a broad class of distributions for which standardized residuals yield asymptotic conditional coverage. We demonstrate that using the Mahalanobis distance induced by a learned local covariance as a non-conformity score provides a closed-form, computationally efficient mechanism ","title":"Multivariate Standardized Residuals for Conformal Prediction","url":"https://arxiv.org/abs/2507.20941","vendor":"arxiv_cs_ai"},"summary":"arXiv:2507.20941v4 Announce Type: replace-cross \nAbstract: 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 non-conformity scores using an 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. Furthermore, we derive a sufficient condition characterizing a broad class of distributions for which standardized residuals yield asymptotic conditional coverage. 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