Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives

Larry Wasserman; Sivaraman Balakrishnan; Tudor Manole

Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives

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arxiv 2506.19025 v1 pith:JYF7KP26 submitted 2025-06-23 math.ST cs.AIcs.LGstat.MEstat.MLstat.TH

Sivaraman Balakrishnan , Tudor Manole , Larry Wasserman This is my paper · ORCID

classification math.STcs.AIcs.LGstat.MEstat.MLstat.TH

keywords optimaltransportadvancesrecentreviewanotherapplicationsbasic

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In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified cost. In this paper we review recent advances in estimating and developing limit theorems for the OT map, using samples from the underlying distributions. We also review parallel lines of work that establish similar results for special cases and variants of the basic OT setup. We conclude with a discussion of key directions for future research with the goal of providing practitioners with reliable inferential tools.

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Sharp Asymptotics for Regularized Optimal Transport
math.AP 2026-07 conditional novelty 7.0 of 10

Sharp small-regularization asymptotics (first-order for EOT, matching-order for p-ROT with 1<p<∞) are established under mild moment/regularity assumptions via a unified quantization-based construction.

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