Related papers: Computational Optimal Transport: Complexity by Acc…
In audio generation evaluation, Fr\'echet Audio Distance (FAD) is a 2-Wasserstein distance with structural constraints for both primitives: the cost is a frozen embedding pullback whose invariance set hides severe artifacts, and the…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. Recent works suggest that these estimators are more statistically efficient than plug-in (linear…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…
Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…
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,…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
Adding entropic regularization to Optimal Transport (OT) problems has become a standard approach for designing efficient and scalable solvers. However, regularization introduces a bias from the true solution. To mitigate this bias while…
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…
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…
We study computing {\em all-pairs shortest paths} (APSP) on distributed networks (the CONGEST model). The goal is for every node in the (weighted) network to know the distance from every other node using communication. The problem admits…
This article describes a set of methods for quickly computing the solution to the regularized optimal transport problem. It generalizes and improves upon the widely-used iterative Bregman projections algorithm (or Sinkhorn--Knopp…
We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…
We study optimal transport between two high-dimensional distributions $\mu,\nu$ in $R^n$ from an algorithmic perspective: given $x \sim \mu$, find a close $y \sim \nu$ in $poly(n)$ time, where $n$ is the dimension of $x,y$. Thus, running…
In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…
We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…
Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
Whilst optimal transport (OT) is increasingly being recognized as a powerful and flexible approach for dealing with fairness issues, current OT fairness methods are confined to the use of discrete OT. In this paper, we leverage recent…
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…