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October 2, 2025Open Access

Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectives

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This review discusses recent advances in optimal transport maps and limit theorems, suggesting reliable inferential tools for practitioners.

The optimal transport map efficiently rearranges mass between probability distributions, minimizing cost.
Recent work estimates optimal transport maps and develops limit theorems, enhancing understanding in this area.
The review also covers similar results in special cases, showing diverse applications of optimal transport.
Future research directions aim to provide practitioners with robust tools for statistical inference in optimal transport.

Balakrishnan et al. (2025) studied this question.

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This review discusses recent advances in optimal transport maps and limit theorems, suggesting reliable inferential tools for practitioners.