arXiv AI
Sep 10

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.

By Kunwoong Kim, Insung Kong, Yongdai Kim
arXiv Machine Learning
Aug 13

Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

arXiv:2608. 11544v1 Announce Type: cross Abstract: We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics.

By Thejani Gamage, Hyemin Gu, Zhizhen Zhang, Ziyu Chen, Markos Katsoulakis, Luc Rey-Bellet
Hugging Face Trending Papers
Aug 12

A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields

In this paper, we propose a local Sinkhorn divergence framework for conditional distribution reconstruction of multidimensional random fields. By utilizing the debiased Sinkhorn divergence, our proposed approach develops a differentiable and computationally efficient local distribution matching objective to train stochastic neural networks (SNNs).