Minimum Volume Optimal Transport for Multivariate Conformal Prediction

Key points

• 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.1
• Using a metric Brenier representation, we derive a volume-based objective that depends explicitly on the Mahalanobis cost matrix and optimize it jointly with the transport map.1
• We establish finite-sample marginal coverage of the output prediction sets and optimality of volume metrics.1
• We further develop an individualized extension that learns covariate-dependent transport metrics, adapting the shape and orientation of prediction sets to heterogeneous conditional distributions.1

Sources (1)

• [1]Minimum Volume Optimal Transport for Multivariate Conformal Prediction
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 10, 01:31 PM

  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.

  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.

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