TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS
成果类型：
Article
署名作者：
Sullivant, Seth; Talaska, Kelli; Draisma, Jan
署名单位：
North Carolina State University; University of Michigan System; University of Michigan; Eindhoven University of Technology
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/09-AOS760
发表日期：
2010
页码：
1665-1685
关键词：
摘要：
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases. Our new trek separation criterion generalizes the familiar d-separation criterion. Proofs are based on the trek rule, the resulting matrix factorizations and classical theorems of algebraic combinatories on the expansions of determinants of path polynomials.