Related papers: Generalized Sinkhorn iterations for regularizing i…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
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…
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…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to…
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…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
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,…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
In this note, we generalize the classical optimal partial transport (OPT) problem by modifying the mass destruction/creation term to function-based terms, introducing what we term ``generalized optimal partial transport'' problems. We then…
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…
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…
The Sinkhorn algorithm is a numerical method for the solution of optimal transport problems. Here, I give a brief survey of this algorithm, with a strong emphasis on its geometric origin: it is natural to view it as a discretization, by…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
Computing optimal transport distances such as the earth mover's distance is a fundamental problem in machine learning, statistics, and computer vision. Despite the recent introduction of several algorithms with good empirical performance,…