V2EX sinkhorn algorithm

Sinkhorn Algorithm

释义 Definition

Sinkhorn 算法:一种用于把非负矩阵通过交替缩放行与列,使其满足指定的行、列边际分布(常见目标是变为“双随机矩阵”)的迭代方法。它在最优传输(Optimal Transport)中尤为常见,用来高效求解带熵正则化的传输计划(也常被称为 Sinkhorn-Knopp 迭代或 iterative proportional fitting 的相关形式)。
(在不同语境下也可指更广义的“矩阵平衡/缩放”算法。)

发音 Pronunciation (IPA)

/sk.hrn l.r.m/

例句 Examples

The Sinkhorn algorithm quickly balances the matrix.
Sinkhorn 算法能快速把矩阵调整到平衡状态。

In entropically regularized optimal transport, we use the Sinkhorn algorithm to compute an approximate transport plan efficiently even for large datasets.
在带熵正则化的最优传输中,我们用 Sinkhorn 算法高效计算近似的传输方案,即使数据集很大也可行。

词源 Etymology

“Sinkhorn”来自美国数学家 Richard Sinkhorn 的姓氏;该算法与 SinkhornKnopp(Sinkhorn 与 Pal Knopp)在 20 世纪提出的矩阵缩放/双随机化结果密切相关。后来在最优传输领域中,随着“熵正则化最优传输”的流行,这类交替行列缩放迭代被广泛用于数值计算,并常直接称为 “Sinkhorn algorithm”。

相关词 Related Words

文学/著作中的出现 Notable Works

  • Marco Cuturi (2013), Sinkhorn Distances: Lightspeed Computation of Optimal Transport(将 Sinkhorn 迭代推广为“Sinkhorn 距离”,推动其在机器学习中的普及)
  • Peyré & Cuturi (2019), Computational Optimal Transport(系统讲解熵正则化 OT 与 Sinkhorn 算法的经典教材)
  • Cédric Villani (2008/2009), Optimal Transport: Old and New(最优传输领域的重要专著,常在相关讨论中提及与之相关的数值方法脉络)
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