arXiv research

Improved online Sinkhorn algorithm for large-scale data processing.

Survey of Sinkhorn algorithm for optimal transport, emphasizing its geometric origins.

Continuous-time Sinkhorn flow generalizes and unifies existing dynamics.

SNS accelerates Sinkhorn algorithm with sparse Newton iterations.

The Sinkhorn flow converges to a Wasserstein mirror gradient flow from the Sinkhorn algorithm.

The Sinkhorn-Knopp derivatives converge with linear rate.

We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show that the complexity of the Sinkhorn algorithm for finding an $\varepsilon$-appr…

This paper refines the Gaussian Sinkhorn algorithm for general multivariate models.

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 screen those components by directly setting them at that value before entering t…

Develops a new algorithm to calibrate signed datasets to specified marginals.

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, it is unknown whether general optimal transport distances can be approximated in …

This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.

Optimal transport with $f$-divergence regularization using generalized Sinkhorn algorithm.

We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation. We consider discret…

New initialization methods speed up Sinkhorn algorithm for OT problems.

Paper analyzes convergence of Sinkhorn algorithm for discrete probability measures on torus.

Paper proposes SinkhornDRL for distributional RL using Sinkhorn divergence and regularized Wasserstein loss.

Optimizes distributions robustly with Sinkhorn distance.

New methods improve stability of Sinkhorn algorithm in machine learning.

A new method reduces the computational cost of Sinkhorn algorithm for OT and UOT problems.

The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for computing this distance grow quadratically with the size of the data, making th…

A new algorithm for training generative models using Sinkhorn divergence.

Paper uses Sinkhorn distances to improve imitation learning effectiveness.

New stability theory for Sinkhorn semigroups with explicit decay rates.

Fast algorithm for online optimization on transport polytopes.

End-to-end Sinkhorn Autoencoder reduces data simulation time with noise generation.

New stability bounds for Sinkhorn's algorithm in entropic optimal transport.

We consider the classical problem of building an arbitrage-free implied volatility surface from bid-ask quotes. We design a fast numerical procedure, for which we prove the convergence, based on the Sinkhorn algorithm that has been recently used to solve efficiently (martingale) optimal transport problems.

We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and the objective function. Since the problem has unbounded domain, the objective func…

We present several new complexity results for the entropic regularized algorithms that approximately solve the optimal transport (OT) problem between two discrete probability measures with at most $n$ atoms. First, we improve the complexity bound of a greedy variant of Sinkhorn, known as \textit{Greenkhorn}, from $\wid…

The Sinkhorn-Knopp algorithm converges quickly but the number of iterations is poorly understood.

This work studies the statistical performance of Sinkhorn iterations in estimating Schrödinger bridges.

New algorithm solves Schrödinger bridge problem with mismatched channels.

Study Hilbert's projective metric for bounded growth functions leading to Sinkhorn's algorithm convergence.

A new algorithm estimates aggregate marginals from noisy data in an online manner.

The Sinkhorn flow is a gradient flow in a nonlocal Wasserstein geometry.

Debiased Wasserstein barycenters improve on entropy regularization in OT.

A new associative memory uses Sinkhorn divergence for efficient pattern retrieval.

OTSeg uses multi-prompt Sinkhorn attention to improve zero-shot semantic segmentation.

Extends geostatistical simulation method to handle multiple variables and large grids.

New algorithm tackles low-rank constraints in optimal transport problems.

Estimating mutual information is an important statistics and machine learning problem. To estimate the mutual information from data, a common practice is preparing a set of paired samples $\{(\mathbf{x}_i,\mathbf{y}_i)\}_{i=1}^n \stackrel{\mathrm{i.i.d.}}{\sim} p(\mathbf{x},\mathbf{y})$. However, in many situations, it…

Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been studied in depth: unbalanced transport, which is robust to the presence of outli…

A new method uses optimal transport for semi-supervised classification.

The paper analyzes stability and convergence rates of entropic and Sinkhorn potentials.

Many problems at the intersection of combinatorics and computer science require solving for a permutation that optimally matches, ranks, or sorts some data. These problems usually have a task-specific, often non-differentiable objective function that data-driven algorithms can use as a learning signal. In this paper, w…

A new method for faster estimation of Wasserstein distance using Sinkhorn divergence.

New algorithm for computing Wasserstein barycenters with guarantees.