6 papers
Another Look at Log-PCA for Probability Measures: A Dynamical Formulation and Statistical Convergence
Peng Xu, Changbo Zhu, Young-Heon Kim +1
This paper is concerned with learning principal variations of random probability measures on under the Wasserstein geometry. We introduce a new dynamical formulation…
A Unified Approach for Computing Wasserstein Barycenters of Discrete and Continuous Measures
Peng Xu, Changbo Zhu, Xiaohui Chen
Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as p…
Smoothed estimation of Wasserstein barycenters
Pengtao Li, Changbo Zhu, Xiaohui Chen
This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality.…
Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysis
Kaheon Kim, Bohan Zhou, Changbo Zhu +1
This paper introduces a new constraint-free concave dual formulation for the Wasserstein barycenter. Tailoring the vanilla dual gradient ascent algorithm to the Sobolev geometry, w…
Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization
Kaheon Kim, Rentian Yao, Changbo Zhu +1
The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability…
Learning Density Evolution from Snapshot Data
Rentian Yao, Atsushi Nitanda, Xiaohui Chen +1
Motivated by learning dynamical structures from static snapshot data, this paper presents a distribution-on-scalar regression approach for estimating the density evolution of a sto…