相关论文: Penalized Barycenters in the Wasserstein Space
In this paper, we focus on computational aspects of the Wasserstein barycenter problem. We propose two algorithms to compute Wasserstein barycenters of $m$ discrete measures of size $n$ with accuracy $\e$. The first algorithm, based on…
Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter…
We investigate barycenters of probability measures on Gromov hyperbolic spaces, toward development of convex optimization in this class of metric spaces. We establish a contraction property (the Wasserstein distance between probability…
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…
The Wasserstein barycenter (WB) is an important tool for summarizing sets of probability measures. It finds applications in applied probability, clustering, image processing, etc. When the measures' supports are finite, computing a…
We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
The primary choice to summarize a finite collection of random objects is by using measures of central tendency, such as mean and median. In the field of optimal transport, the Wasserstein barycenter corresponds to the Fr\'{e}chet or…
In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation…
Wasserstein barycenter is the centroid of a collection of discrete probability distributions which minimizes the average of the $\ell_2$-Wasserstein distance. This paper focuses on the computation of Wasserstein barycenters under the case…
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…
The consensus problem -- achieving agreement among a network of agents -- is a central theme in both theory and applications. Recently, this problem has been extended from Euclidean spaces to the space of probability measures, where the…
This paper provides rates of convergence for empirical (generalised) barycenters on compact geodesic metric spaces under general conditions using empirical processes techniques. Our main assumption is termed a variance inequality and…
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…
We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…
We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…
Collecting and aggregating information from several probability measures or histograms is a fundamental task in machine learning. One of the popular solution methods for this task is to compute the barycenter of the probability measures…
A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…
We introduce weak barycenters of a family of probability distributions, based on the recently developed notion of optimal weak transport of mass by Gozlanet al. (2017) and Backhoff-Veraguas et al. (2020). We provide a theoretical analysis…