Related papers: Parameterized Wasserstein mean with its properties
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that…
Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…
In this paper, we expand upon the theory of trend filtering by introducing the use of the Wasserstein metric as a means to control the amount of spatiotemporal variation in filtered time series data. While trend filtering utilizes…
We introduce a modified Benamou-Brenier type approach leading to a Wasserstein type distance that allows global invariance, specifically, isometries, and we show that the problem can be summarized to orthogonal transformations. This…
A recurring obstacle in the study of Wasserstein gradient flow is the lack of convexity of the square Wasserstein metric. In this paper, we develop a class of transport metrics that have better convexity properties and use these metrics to…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
The concepts of mean (i.e., average) and covariance of a random variable are fundamental in statistics, and are used to solve real-world problems such as those that arise in robotics, computer vision, and medical imaging. On matrix Lie…
Archetypal analysis is an unsupervised machine learning method that summarizes data using a convex polytope. In its original formulation, for fixed k, the method finds a convex polytope with k vertices, called archetype points, such that…
We use a new method via $p$-Wasserstein bounds to prove Cram\'er-type moderate deviations in (multivariate) normal approximations. In the classical setting that $W$ is a standardized sum of $n$ independent and identically distributed…
We study the Wasserstein gradient flow of the Sinkhorn divergence when both the source and the target are Gaussian distributions. We prove the existence of a flow that stays in the class of Gaussian distributions, and is unique in the…
We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…
We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…
We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
In this paper, we define the generalized Wasserstein distance for sets of Borel probability measures and demonstrate that the weak convergence of sublinear expectations can be characterized by means of this distance.
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…
We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the Circular Law. For general entry distributions, we obtain a nearly optimal rate of convergence in 1-Wasserstein…
We provide new bounds for the rate of convergence of the multivariate Central Limit Theorem in Wasserstein distances of order $p \geq 2$. In particular, we obtain what we conjecture to be the asymptotically optimal rate whenever the density…
We compute quantitative bounds for measuring the discrepancy between the distribution of two min-max statistics involving either pairs of Gaussian random matrices, or one Gaussian and one Gaussian-subordinated random matrix. In the fully…
The asymptotic behaviour of empirical measures has been studied extensively. In this paper, we consider empirical measures of given subordinated processes on complete (not necessarily compact) and connected Riemannian manifolds with…