A0521
Title: Conformal inference for multivariate mixed outcomes via fairness-constrained optimal transport
Authors: Larry Han - Northeastern University (United States) [presenting]
Chenyin Gao - Google LLC (United States)
Abstract: Many decisions require reasoning over multiple outcomes simultaneously, especially when outcomes are of mixed type (e.g., continuous and discrete). Existing conformal inference methods for multivariate prediction often assume continuous outcomes, overlook fairness across subgroups, or yield prediction regions that are difficult to interpret. A conditional latent highest density region (CL-HDR) is introduced, a new framework for conformal prediction with multivariate mixed outcomes that ensures finite-sample coverage, supports customizable fairness constraints, and yields efficient prediction regions with minimal volume. The method leverages optimal transport and normalizing flows to construct multivariate ranks and uses input convex neural networks to approximate the transport map. To guarantee group-conditional coverage, a functional synchronization procedure is proposed based on Wasserstein barycenters, enabling fairness objectives to be encoded directly into the prediction set construction. Across synthetic and real-world datasets, CL-HDR produces smaller, more interpretable prediction regions than existing approaches while achieving subgroup-level validity.
