高维最优运输问题的基于投影的技术

IF 4.4 2区 数学 Q1 STATISTICS & PROBABILITY
Jingyi Zhang, Ping Ma, Wenxuan Zhong, Cheng Meng
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引用次数: 11

摘要

最优运输(OT)方法寻求两个概率测度之间的转换图(或计划),使得转换具有最小的运输成本。在一定的功率变换下,这样的最小运输成本被称为Wasserstein距离。近年来,OT方法在统计学、机器学习和计算机科学中引起了极大的关注,尤其是在深度生成神经网络中。尽管应用广泛,但由于维数的诅咒,高维Wasserstein距离的估计是一个众所周知的具有挑战性的问题。有一些基于前沿投影的技术可以解决高维OT问题。介绍了这类技术的三种主要方法,分别是切片方法、迭代投影方法和投影鲁棒OT方法。审查结束时讨论了悬而未决的挑战。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Projection‐based techniques for high‐dimensional optimal transport problems
Optimal transport (OT) methods seek a transformation map (or plan) between two probability measures, such that the transformation has the minimum transportation cost. Such a minimum transport cost, with a certain power transform, is called the Wasserstein distance. Recently, OT methods have drawn great attention in statistics, machine learning, and computer science, especially in deep generative neural networks. Despite its broad applications, the estimation of high‐dimensional Wasserstein distances is a well‐known challenging problem owing to the curse‐of‐dimensionality. There are some cutting‐edge projection‐based techniques that tackle high‐dimensional OT problems. Three major approaches of such techniques are introduced, respectively, the slicing approach, the iterative projection approach, and the projection robust OT approach. Open challenges are discussed at the end of the review.
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CiteScore
6.20
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