Reproduce “Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization” on OpenResearch

About this paper

Naomi Desobry, Elnura Zhalieva, Souhaib Ben Taieb

A differentiable regularization framework is presented to enforce multivariate calibration in probabilistic regression models by penalizing deviations of pre-rank projected Probability Integral Transforms from uniformity. This approach improves calibration across diverse multi-output datasets, including with a novel PCA-based pre-rank, without compromising predictive accuracy.

Key insights

• Explicit, differentiable regularization based on pre-rank functions can effectively enforce multivariate calibration during model training, moving beyond mere diagnostics.
• Joint regularization addressing both marginal and pre-rank calibration is essential for comprehensive uncertainty quantification, as single pre-rank calibration does not guarantee marginal calibration.
• The PCA-based pre-rank offers a scalable and effective strategy for higher-dimensional problems, providing a good trade-off between calibration quality and computational cost by focusing on directions of maximal variance.

Summary by alphaXiv.