7 papers
Energy-Guided Learning for Heat Equation with Noisy Source: Optimal Estimation and Generalization Bounds
Zixiang Zhou, Xiaohui Chen, Shanghua Teng
Data and the governing partial differential equations (PDEs) of continuous-time dynamical systems provide rich structure for statistical learning. A central challenge is how to int…
Quantitative Stability and Sample Complexity for Regularized Gromov-Wasserstein Distance
Pengtao Li, Xiaohui Chen
The Gromov-Wasserstein (GW) distance provides a principled framework for comparing two probability distributions supported on different metric spaces by matching their individual i…
Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters
Pengtao Li, Alberto González-Sanz, Xiaohui Chen
Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional a…
Hierarchy of discriminative power and complexity in learning quantum ensembles
Jian Yao, Pengtao Li, Xiaohui Chen +1
Distance metrics are central to machine learning, yet distances between ensembles of quantum states remain poorly understood due to fundamental quantum measurement constraints. We…
Neural Local Wasserstein Regression
Inga Girshfeld, Xiaohui Chen
We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a gl…
Sample complexity and weak limits of nonsmooth multimarginal Schrödinger system with application to optimal transport barycenter
Pengtao Li, Xiaohui Chen
Multimarginal optimal transport (MOT) has emerged as a useful framework for many applied problems. However, compared to the well-studied classical two-marginal optimal transport th…
Convergence Analysis of the Wasserstein Proximal Algorithm beyond Geodesic Convexity
Shuailong Zhu, Xiaohui Chen
The proximal algorithm is a powerful tool to minimize nonlinear and nonsmooth functionals in a general metric space. Motivated by the recent progress in studying the training dynam…