Related papers: Approximating the Optimal Transport Plan via Parti…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
This paper is concerned with the theoretical and computational development of a new class of nonlinear filtering algorithms called the optimal transport particle filters (OTPF). The algorithm is based on a recently introduced variational…
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…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…
We study estimators of the optimal transport (OT) map between two probability distributions. We focus on plugin estimators derived from the OT map between estimates of the underlying distributions. We develop novel stability bounds for OT…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
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…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
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…
We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory…
This paper studies the Partial Optimal Transport (POT) problem between two unbalanced measures with at most $n$ supports and its applications in various AI tasks such as color transfer or domain adaptation. There is hence the need for fast…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…