English
Related papers

Related papers: Distributional barycenter problem through data-dri…

200 papers

Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…

Optimization and Control · Mathematics 2019-05-13 Andrew M. Stuart , Marie-Therese Wolfram

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…

Optimization and Control · Mathematics 2020-01-22 Dongdong Ge , Haoyue Wang , Zikai Xiong , Yinyu Ye

We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we propose a sampling gradient quantization scheme that allows…

Optimization and Control · Mathematics 2020-10-28 Roman Krawtschenko , César A. Uribe , Alexander Gasnikov , Pavel Dvurechensky

We consider a variant of the berth allocation problem-i.e., the multi-port berth allocation problem-aimed at assigning berthing times and positions to vessels in container terminals. This variant involves optimizing vessel travel speeds…

Optimization and Control · Mathematics 2021-10-05 Bernardo Martin-Iradi , Dario Pacino , Stefan Ropke

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Numerical Analysis · Mathematics 2015-09-15 Adam M. Oberman , Yuanlong Ruan

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…

Machine Learning · Computer Science 2018-06-08 Sebastian Claici , Edward Chien , Justin Solomon

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:…

Machine Learning · Computer Science 2017-11-15 Matthew Staib , Sebastian Claici , Justin Solomon , Stefanie Jegelka

Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…

Optimization and Control · Mathematics 2023-01-25 Florian Beier , Johannes von Lindheim , Sebastian Neumayer , Gabriele Steidl

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…

Optimization and Control · Mathematics 2020-06-26 Isabel Haasler , Rahul Singh , Qinsheng Zhang , Johan Karlsson , Yongxin Chen

Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…

Optimization and Control · Mathematics 2019-04-10 Rui Zhang , Quanyan Zhu

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…

Optimization and Control · Mathematics 2020-09-11 Nazarii Tupitsa , Pavel Dvurechensky , Alexander Gasnikov , César A. Uribe

This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…

Computer Vision and Pattern Recognition · Computer Science 2013-07-23 Sira Ferradans , Nicolas Papadakis , Gabriel Peyré , Jean-François Aujol

This paper outlines the ideas behind developing a graph-based heuristic-driven routing algorithm designed for a particular instance of a goods transportation problem with a single good type. The proposed algorithm solves the optimization…

Artificial Intelligence · Computer Science 2021-02-16 Mikhail Shchukin , Aymen Ben Said , Andre Lobo Teixeira

The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of discrete probability measures. Although an exact barycenter is computable through linear programming, the underlying linear program can be…

Optimization and Control · Mathematics 2022-02-09 Steffen Borgwardt , Stephan Patterson

We study the problem of learning a real-valued function that satisfies the Demographic Parity constraint. It demands the distribution of the predicted output to be independent of the sensitive attribute. We consider the case that the…

Machine Learning · Statistics 2020-06-24 Evgenii Chzhen , Christophe Denis , Mohamed Hebiri , Luca Oneto , Massimiliano Pontil

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…

Optimization and Control · Mathematics 2023-07-26 Olga Yufereva , Michael Persiianov , Pavel Dvurechensky , Alexander Gasnikov , Dmitry Kovalev

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…

Machine Learning · Statistics 2023-03-13 Elsa Cazelles , Felipe Tobar , Joaquín Fontbona

The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the…

Optimization and Control · Mathematics 2026-02-18 Hongkang Yang , Esteban G. Tabak

The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in the machine learning and computer vision communities as a…

Machine Learning · Statistics 2026-03-31 David Gentile , James M. Murphy

A randomized version of the recently developed barycenter method for derivative--free optimization has desirable properties of a gradient search. We developed a complex version to avoid evaluations at high--gradient points. The method,…

Optimization and Control · Mathematics 2021-02-23 Felipe M Pait