6 papers
Gaussian-Restricted Barycenters for KL-Unbalanced Optimal Transport: Variational Theory and Fixed-Point Convergence
Jiaping Yang, Yunxin Zhang
We study Gaussian-restricted barycenters for quadratic two-sided Kullback--Leibler unbalanced optimal transport with independent marginal penalties and no coupling entropy. Exact p…
High-Dimensional Spectral Limits for Gaussian KL-Unbalanced Optimal Transport
Jiaping Yang, Yunxin Zhang
We study high-dimensional random-matrix limits of Gaussian Kullback--Leibler unbalanced optimal transport (KL-UOT). Under equal marginal penalties, the covariance action admits an…
Two-Sample Inference for Gaussian-Smoothed Wasserstein Costs with Finite Moments
Jiaping Yang, Yunxin Zhang
Gaussian smoothing has emerged as an effective technique for reducing the sample complexity of optimal transport. In this paper, we study the two-sample plug-in estimator of the Ga…
Bures Geodesics and Restricted Barycenters for Kronecker Positive Definite Matrices
Jiaping Yang, Yunxin Zhang
We study the extrinsic Bures--Wasserstein geometry of the determinant-normalized Kronecker model $\mcK_n=\{V\ot U:U,V\in\Sp^n,\ \det U=1\}\subset\Sp^{n^2}$, asking when the ambient…
Closed Forms for Gaussian Kullback--Leibler Unbalanced Optimal Transport without Coupling Entropy
Jiaping Yang, Yunxin Zhang
We obtain an explicit solution for the static Kullback--Leibler (KL) unbalanced optimal transport problem between finite non-degenerate Gaussian measures with quadratic cost, two i…
General Divergence Regularized Optimal Transport: Sample Complexity and Central Limit Theorems
Jiaping Yang, Yunxin Zhang
We study empirical divergence-regularized optimal transport on arbitrary Polish spaces. For bounded continuous costs and dual-regular conjugates , we establish…