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Deep Barycentric Regression for Optimal Transport Map Estimation and its Statistical Optimality

arXiv · AI, language, vision and robotics · article · Sep 6, 2026 · UTC

The optimal transport (OT) map provides a geometric transformation for aligning probability distributions and has become a useful tool in machine learning. However, existing estimators of the OT map still exhibit a gap between sharp statistical guarantees and practical parametric estimation based on stable training objectives. Theoretical estimators achieve minimax optimal convergence rates, but they are typically nonparametric and can incur demanding implementation design or inference costs. Practical estimators are parametric and scalable, but their statistical guarantees remain underexplore

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