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

תקציר מקורי באנגליתarXiv:2609.06598v1 Announce Type: cross Abstract: 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 underexplored, and their min-max, adversarial-like training objectives can be sensitive to optimization algorithms. We propose BROT (Barycentric Regression for OT