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Wasserstein barycenters define averages of probability measures in a geometrically meaningful way. Their use is increasingly popular in applied fields, such as image, geometry or language processing. In these fields however, the probability…
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…
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…
Discrete Wasserstein barycenters correspond to optimal solutions of transportation problems for a set of probability measures with finite support. Discrete barycenters are measures with finite support themselves and exhibit two favorable…
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 unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…
We consider a multimarginal optimal transport, which includes as a particular case the Wasserstein barycenter problem. In this problem one has to find an optimal coupling between $m$ probability measures, which amounts to finding a tensor…
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…
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…
Algorithmic Fairness is an established field in machine learning that aims to reduce biases in data. Recent advances have proposed various methods to ensure fairness in a univariate environment, where the goal is to de-bias a single task.…
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…
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)…
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 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…
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…
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…
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…
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 study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…
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…