Computations of Optimal Transport Distance with Fisher Information Regularization

被引：32

作者：

Li, Wuchen ^{[1
]}

Yin, Penghang ^{[1
]}

Osher, Stanley ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Los Angeles, CA 90095 USA

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2018年 / 75卷 / 03期

基金：

美国国家科学基金会;

关键词：

Optimal transport; Fisher information; Schrodinger bridge problem; Newton's method;

D O I：

10.1007/s10915-017-0599-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is shown to be smooth and strictly convex, thus many classical fast algorithms are available. In this paper, we adopt Newton's method, which converges to the minimizer with a quadratic rate. Several numerical examples are provided.

引用

页码：1581 / 1595

页数：15

共 32 条

[1]

[Anonymous], 2017, ARXIV170507583

[2]

[Anonymous], ARXIV170104841

[3]

Benamou JD, 2000, NUMER MATH, V84, P375, DOI 10.1007/s002119900117

[4]

Carlen E., 2014, Diffusion, Quantum Theory and Radically Elementary Math- ematics, V47, P117