Calibrated Multivariate Distributional Regression with Pre-Rank Regularization
This work addresses the problem of multivariate calibration for researchers and practitioners in machine learning, offering an incremental advance by extending pre-rank functions from diagnostics to training regularization.
The paper tackles the challenge of achieving multivariate calibration in probabilistic prediction by proposing a regularization-based method that enforces calibration during training using pre-rank functions, and introduces a PCA-based pre-rank for detecting dependence-structure misspecifications. Results from simulations and 18 real-world datasets show substantial improvements in multivariate calibration without compromising predictive accuracy.
The goal of probabilistic prediction is to issue predictive distributions that are as informative as possible, subject to being calibrated. Despite substantial progress in the univariate setting, achieving multivariate calibration remains challenging. Recent work has introduced pre-rank functions, scalar projections of multivariate forecasts and observations, as flexible diagnostics for assessing specific aspects of multivariate calibration, but their use has largely been limited to 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 simulation studies and experiments on 18 real-world multi-output regression datasets, we show that the proposed approach substantially improves multivariate pre-rank calibration without compromising predictive accuracy, and that the PCA pre-rank reveals dependence-structure misspecifications that are not detected by existing pre-ranks.