相关论文: Sampling From the Wasserstein Barycenter
In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector by distribution. The…
In this paper, we focus on the analysis of the regularized Wasserstein barycenter problem. We provide uniqueness and a characterization of the barycenter for two important classes of probability measures: (i) Gaussian distributions and (ii)…
The Wasserstein barycenter extends the Euclidean mean to the space of probability measures by minimizing the weighted sum of squared 2-Wasserstein distances. We develop a free-support algorithm for computing Wasserstein barycenters that…
We develop an estimator-based stochastic fixed-point framework for approximately computing the 2-Wasserstein barycenter of continuous, non-parametric probability measures. Notably, we provide the first rigorous convergence analysis for…
This paper studies the statistical estimation of exact Wasserstein barycenters. Existing non-asymptotic results for empirical barycenters exhibit a severe curse of dimensionality. Motivated by the semi-dual formulation of the barycenter…
The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…
This paper presents an efficient algorithm for the progressive approximation of Wasserstein barycenters of persistence diagrams, with applications to the visual analysis of ensemble data. Given a set of scalar fields, our approach enables…
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. Previous research has demonstrated that various…
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…
Consider a multi-agent system whereby each agent has an initial probability measure. In this paper, we propose a distributed algorithm based upon stochastic, asynchronous and pairwise exchange of information and displacement interpolation…
Wasserstein barycentres represent average distributions between multiple probability measures for the Wasserstein distance. The numerical computation of Wasserstein barycentres is notoriously challenging. A common approach is to use…
In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph.
In this paper, we introduce a generalization of the Wasserstein barycenter, to a case where the initial probability measures live on different subspaces of R^d. We study the existence and uniqueness of this barycenter, we show how it is…
Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
This paper is focused on the statistical analysis of probability measures $\nu_{1},\ldots,\nu_{n}$ on $\mathbb{R}$ that can be viewed as independent realizations of an underlying stochastic process. We consider the situation of practical…
Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has…
This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random…