Minimum Volume Optimal Transport for Multivariate Conformal Prediction
Optimal transport (OT) enables multivariate conformal prediction (CP) to construct flexible prediction sets that reflect the underlying complex distributional geometry while retaining distribution-free coverage guarantees. Existing OT-based methods typically rely on a fixed Euclidean transport cost, which can be suboptimal in terms of the volume of prediction sets. We propose Minimum-Volume OTCP, a framework that learns a Mahalanobis ground cost to directly minimize prediction-region volume over a class of positive-definite metrics. Using a metric Brenier representation, we derive a volume-based objective that depends explicitly on the Mahalanobis cost matrix and optimize it jointly with ...
| Authors | Chuchen Zhang, Haojie Ren, Zhaojun Wang et al. |
|---|---|
| Primary category | stat.ML |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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