arXiv AI September 10, 2026 By Kunwoong Kim, Insung Kong, Yongdai Kim

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

The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.

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