Author

Xiao-Hui Chen

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Preprint Oct 2026

Quantitative Stability and Sample Complexity for Regularized Gromov-Wasserstein Distance

The Gromov-Wasserstein (GW) distance provides a principled framework for comparing two probability distributions supported on different metric spaces by matching their individual intrinsic geometric structures. In practice, the GW distance is estimated from finite samples and often incorporates regularization for stati...

Peng-Tao Li, Xiao-Hui Chen · 0 citations

Preprint Sep 2026

Central limit theorems and bootstrap for sparse regularized multimarginal optimal transport and barycenters

Wasserstein barycenters are a fundamental tool for the analysis of distribution-valued data, but their computation and statistical analysis become challenging in high-dimensional and multi-sample settings. The unregularized barycenter problem is computationally demanding and suffers severely from the curse of dimension...

Peng-Tao Li, Alberto González-Sanz, Xiao-Hui Chen · 0 citations

#machine learning Preprint Oct 2026

Energy-Guided Learning for Heat Equation with Noisy Source: Optimal Estimation and Generalization Bounds

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 integrate data with PDE constraints in a principled way to improve generalization. In this paper, we characterize the statistical estimation an...

Zi-Xian Zhou, Xiao-Hui Chen, Shang-Hua Teng · 0 citations