Related papers: Randomised Wasserstein Barycenter Computation: Res…
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement…
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…
This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…
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…
Divide-and-conquer based methods for Bayesian inference provide a general approach for tractable posterior inference when the sample size is large. These methods divide the data into smaller subsets, sample from the posterior distribution…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…
In this paper, a regularization of Wasserstein barycenters for random measures supported on $\mathbb{R}^{d}$ is introduced via convex penalization. The existence and uniqueness of such barycenters is first proved for a large class of…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
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…
Barycentric averaging is a principled way of summarizing populations of measures. Existing algorithms for estimating barycenters typically parametrize them as weighted sums of Diracs and optimize their weights and/or locations. However,…
Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…
Computing Wasserstein barycenters is a fundamental geometric problem with widespread applications in machine learning, statistics, and computer graphics. However, it is unknown whether Wasserstein barycenters can be computed in polynomial…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
The so-called \emph{simplified} Wasserstein barycenter problem, also known as the cheapest hub problem, consists in selecting one point from each of $k$ given sets, each set consisting of $n$ points, with the aim of minimizing the sum of…
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…
A randomized version of the recently developed barycenter method for derivative-free optimization has desirable properties of a gradient search. We develop a complex version to avoid evaluations at high-gradient points. The method,…
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…
In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation…
Computing Wasserstein barycenters (a.k.a. Optimal Transport barycenters) is a fundamental problem in geometry which has recently attracted considerable attention due to many applications in data science. While there exist polynomial-time…
Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the…