Multi-Output Conformal Regression: A Unified View with Comparisons

Matteo Fontana (Royal Holloway, University of London)

Wednesday 5th March 11:00-12:00 Maths 311B

Abstract

Quantifying uncertainty in multivariate regression is crucial across many real-world applications. However, existing approaches for constructing prediction regions often struggle to capture complex dependencies, lack formal coverage guarantees, or incur high computational costs. Conformal prediction addresses these challenges by providing a robust, distribution-free framework with finite-sample coverage guarantees. In this study, we offer a unified comparison of multi-output conformal techniques, highlighting their properties and interrelationships. Leveraging these insights, we propose two families of conformity scores that achieve asymptotic conditional coverage: one can be paired with any generative model, while the other reduces computational overhead by utilizing invertible generative models. We then present a large-scale empirical analysis on 32 tabular datasets, comparing all methods under a consistent code base to ensure fairness and reproducibility

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