Calibrated Multivariate Distributional Regression with Pre-Rank Regularization

Aya LAAJIL, Elnura Zhalieva, Naomi Desobry, Souhaib Ben Taieb

Keywords: Probabilistic Calibration, Multivariate Calibration, pre-rank functions, Regularization

Abstract: The goal of probabilistic prediction is to issue predictive distributions that are as informative as possible, subject to being calibrated. Whereas univariate calibration is well understood, achieving multivariate calibration remains challenging. Recent work has introduced pre-rank functions, scalar projections of multivariate predictions and observations, as diagnostics for multivariate calibration, but they are mainly used for post-hoc evaluation. We propose a regularization-based calibration method that enforces multivariate calibration during training of multivariate distributional regression models using pre-rank functions. We further introduce a novel PCA-based pre-rank that projects predictions onto principal directions of the predictive distribution. Through simulations and experiments on 18 real-world datasets, the proposed approach improves multivariate pre-rank calibration without compromising predictive accuracy, and our PCA pre-rank reveals dependence-structure misspecifications that are not detected by existing pre-ranks.

Submission Number: 22