Title: FACTOR: Fairness-Aligned Conformal Transport for Multivariate Mixed Outcomes
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: conformal prediction, multivariate outcomes, fairness, optimal transport, clinical decision-making

Abstract: 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 \textsc{factor} (\emph{Fairness-Aligned Conformal Transport for Optimal Regions}), a framework for constructing compact and equitable prediction regions. \textsc{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, \textsc{factor} consistently achieves target coverage with reduced region volume and subgroup disparities (measured by KS distance) relative to state-of-the-art baselines under competitive runtime. The method also produces interpretable visualizations and conditional summaries, making \textsc{factor} a practical tool for uncertainty quantification in multivariate, mixed-outcome settings.

TL;DR: We develop FACTOR, a conformal prediction framework for compact, fair, and distribution-free prediction regions for multivariate mixed outcomes.