Positive Curvature and Hamiltonian Monte Carlo

被引：0

作者：

Seiler, Christof ^{[1
]}

Rubinstein-Salzedo, Simon ^{[1
]}

Holmes, Susan ^{[1
]}

机构：

[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

来源：

ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 27 (NIPS 2014) | 2014年 / 27卷

基金：

瑞士国家科学基金会;

关键词：

D O I：

暂无

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The Jacobi metric introduced in mathematical physics can be used to analyze Hamiltonian Monte Carlo (HMC). In a geometrical setting, each step of HMC corresponds to a geodesic on a Riemannian manifold with a Jacobi metric. Our calculation of the sectional curvature of this HMC manifold allows us to see that it is positive in cases such as sampling from a high dimensional multivariate Gaussian. We show that positive curvature can be used to prove theoretical concentration results for HMC Markov chains.

引用

页数：9

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