Related papers: Parallel Streaming Wasserstein Barycenters
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…
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…
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 study the problem of model aggregation within the Wasserstein space for probability measures on the real line. Given a fixed finite collection of candidate probability models, we consider the associated class of Wasserstein barycenters…
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…
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…
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 distributions. Computation of the unregularized barycenter…
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…
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…
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…
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive…
We consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
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…
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…
We present a framework to simultaneously align and smooth data in the form of multiple point clouds sampled from unknown densities with support in a d-dimensional Euclidean space. This work is motivated by applications in bioinformatics…
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 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…
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…