Related papers: HOT: An Efficient Halpern Accelerating Algorithm f…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Computationally solving multi-marginal optimal transport (MOT) with squared Euclidean costs for $N$ discrete probability measures has recently attracted considerable attention, in part because of the correspondence of its solutions with…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from…
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…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…
We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
In this paper, we propose an accelerated version for the Sinkhorn algorithm, which is the reference method for computing the solution to Entropic Optimal Transport. Its main draw-back is the exponential slow-down of convergence as the…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
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…