Related papers: Accelerating Sinkhorn Algorithm with Sparse Newton…
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 second-order optimization, a potential bottleneck can be computing the Hessian matrix of the optimized function at every iteration. Randomized sketching has emerged as a powerful technique for constructing estimates of the Hessian which…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…
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…
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…
Entropic optimal transport problems play an increasingly important role in machine learning and generative modelling. In contrast with optimal transport maps which often have limited applicability in high dimensions, Schrodinger bridges can…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote…
The Sinkhorn--Knopp (SK) algorithm is a cornerstone method for matrix scaling and entropically regularized optimal transport (EOT). Despite its empirical efficiency, existing theoretical guarantees to achieve a target marginal accuracy…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
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…
We propose Acc-Sinkhorn, a simple accelerated variant of Sinkhorn for entropy-regularized optimal transport (EOT). The method is derived from a bilevel optimization view: Sinkhorn row scaling solves the inner variable $u$ exactly and…
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
Sparsity-constrained optimization underlies many problems in signal processing, statistics, and machine learning. State-of-the-art hard-thresholding (HT) algorithms rely on an appropriately selected continuous step-size parameter to ensure…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
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…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
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…