学习最优输运度量下的概率度量

Sep, 2012

Learning Probability Measures with respect to Optimal Transport Metrics

Guillermo D. Canas, Lorenzo Rosasco

TL;DR通过优化传输度量，在嵌入Hilbert空间的流形上估计一种衡量方法，并将量化优化和学习理论联系起来，为无监督学习中经典算法（k-means）的性能提供新的概率界限。在分析的过程中，我们得出了新的下界和概率上界，这些上下界适用于广泛的测度范围。

Abstract

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transpo