Related papers: Discrete Wasserstein Barycenters: Optimal Transpor…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
In this paper we propose to perform model ensembling in a multiclass or a multilabel learning setting using Wasserstein (W.) barycenters. Optimal transport metrics, such as the Wasserstein distance, allow incorporating semantic side…
In this paper, we address a fundamental limitation of the classical Wasserstein barycenter -- its sensitivity to outliers and its reliance on finite first/second moment assumptions. To overcome these issues, we propose the robust…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric…
In this article, we study Wasserstein-type metrics and corresponding barycenters for mixtures of a chosen subset of probability measures called atoms hereafter. In particular, this works extends what was proposed by Delon and Desolneux [A…
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…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…
We introduce a weak notion of barycenter of a probability measure $\mu$ on a metric measure space $(X, d, {\bf m})$, with the metric $d$ and reference measure ${\bf m}$. Under the assumption that optimal transport plans are given by…
We propose the linear barycentric coding model (LBCM) which utilizes the linear optimal transport (LOT) metric for analysis and synthesis of probability measures. We provide a closed-form solution to the variational problem characterizing…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
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…
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…
Optimal transport maps between two probability distributions $\mu$ and $\nu$ on $\mathbb{R}^d$ have found extensive applications in both machine learning and statistics. In practice, these maps need to be estimated from data sampled…
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…