Year: 2023
Type: preprint
Abstract: 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 between two discrete distributions of size $n$. Given the cost matrix $C=AA^\top$ where $A \in \mathbb{R}^{n \times d}$, we proposed a faster Sinkhorn's Algorithm to approximate the OT distance when matrix $A$ has treewidth $τ$. To approximate the OT distance, our algorithm improves the state-of-the-art results [Dvurechensky, Gasnikov, and Kroshnin ICML 2018] from $\widetilde{O}(ε^{-2} n^2)$ time to $\widetilde{O}(ε^{-2} n τ)$ time.
Source: arXiv (Cornell University)
Authors: Song, Zhao, Zhou, Tianyi
Institution: Adobe Systems (United States)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4317464013