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The Sinkhorn algorithm is a widely used method for solving the optimal transport problem, and the Greenkhorn algorithm is one of its variants. While there are modified versions of these two algorithms whose computational complexities are…
Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…
Entropic regularized optimal transport (OT) via the Sinkhorn algorithm has become a fundamental tool in machine learning, yet existing implementations either suffer from numerical instability for small regularization parameters or incur…
Computing optimal transport (OT) distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. In this paper, we study the problem of approximating the general OT distance…
The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
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 propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
Sinkhorn algorithm has been used pervasively to approximate the solution to optimal transport (OT) and unbalanced optimal transport (UOT) problems. However, its practical application is limited due to the high computational complexity. To…
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) 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…
Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…
Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…