Fairness-Aligned Conformal Transport for Multivariate Mixed Outcomes

Thomas M. Menino Convention & Exhibition Center 

In high-stakes domains, decisions often hinge on jointly predicting multiple, correlated outcomes of mixed type (continuous, ordinal, categorical). Existing multivariate conformal methods impose restrictive geometric assumptions, perform poorly with mixed outcomes, or lack subgroup-conditional guarantees, leading to inflated prediction regions and uneven coverage. We propose FACTOR (Fairness-Aligned Conformal Transport for Optimal Regions), a framework for constructing compact and equitable prediction regions. FACTOR learns an optimal-transport map in a latent space via normalizing flows with input-convex neural networks, providing a principled multivariate ranking without shape constraints. To enforce fairness, we synchronize latent-space ranks across subgroups, yielding distribution-free marginal coverage and a finite-sample O(1/N) bound on subgroup calibration error. A sliding-window cutoff procedure then minimizes prediction region volume while preserving validity. Empirically, on synthetic and six real-world benchmarks, FACTOR consistently achieves target coverage with reduced region volume and subgroup disparities (KS distance) relative to state-of-the-art baselines.

Conformal prediction

Optimal transport

Fairness

Multivariate outcomes 

Section on Statistical Learning and Data Science