Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration
This addresses a fundamental computational bottleneck in machine learning, statistics, and computer vision, providing a near-linear time solution for optimal transport approximation.
The paper tackles the problem of approximating optimal transport distances in near-linear time, demonstrating that Sinkhorn Distances achieve this goal and introducing Greenkhorn, a new algorithm that outperforms Sinkhorn in practice with significant speed improvements.
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 near-linear time. This paper demonstrates that this ambitious goal is in fact achieved by Cuturi's Sinkhorn Distances. This result relies on a new analysis of Sinkhorn iteration, which also directly suggests a new greedy coordinate descent algorithm, Greenkhorn, with the same theoretical guarantees. Numerical simulations illustrate that Greenkhorn significantly outperforms the classical Sinkhorn algorithm in practice.