TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS

被引:56
|
作者
Sullivant, Seth [1 ]
Talaska, Kelli [2 ]
Draisma, Jan [3 ,4 ]
机构
[1] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
[3] TU Eindhoven, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
[4] Ctr Wiskunde & Informat, Amsterdam, Netherlands
来源
ANNALS OF STATISTICS | 2010年 / 38卷 / 03期
基金
美国国家科学基金会;
关键词
Graphical model; Bayesian network; Gessel-Viennot-Lindstrom lemma; trek rule; linear regression; conditional independence;
D O I
10.1214/09-AOS760
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
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.
引用
收藏
页码:1665 / 1685
页数:21
相关论文
共 50 条
  • [31] Standard errors for the parameters of graphical Gaussian models
    Roverato, A
    Whittaker, J
    STATISTICS AND COMPUTING, 1996, 6 (03) : 297 - 302
  • [32] Conditional Matrix Flows for Gaussian Graphical Models
    Negri, Marcello Massimo
    Torres, Fabricio Arend
    Roth, Volker
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 36 (NEURIPS 2023), 2023,
  • [33] Learning Latent Variable Gaussian Graphical Models
    Meng, Zhaoshi
    Eriksson, Brian
    Hero, Alfred O., III
    INTERNATIONAL CONFERENCE ON MACHINE LEARNING, VOL 32 (CYCLE 2), 2014, 32 : 1269 - 1277
  • [34] LEARNING GAUSSIAN GRAPHICAL MODELS USING DISCRIMINATED HUB GRAPHICAL LASSO
    Li, Zhen
    Bai, Jingtian
    Zhou, Weilian
    2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), 2018, : 2471 - 2475
  • [35] Model selection for inferring Gaussian graphical models
    De Canditiis, Daniela
    Cirulli, Silvia
    COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2023, 52 (12) : 6084 - 6095
  • [36] Structured regularization for conditional Gaussian graphical models
    Julien Chiquet
    Tristan Mary-Huard
    Stéphane Robin
    Statistics and Computing, 2017, 27 : 789 - 804
  • [37] Gaussian graphical models with toric vanishing ideals
    Pratik Misra
    Seth Sullivant
    Annals of the Institute of Statistical Mathematics, 2021, 73 : 757 - 785
  • [38] On some algorithms for estimation in Gaussian graphical models
    Hojsgaard, S.
    Lauritzen, S.
    BIOMETRIKA, 2024, 111 (04)
  • [39] Graphical Gaussian models with edge and vertex symmetries
    Hojsgaard, Soren
    Lauritzen, Steffen L.
    JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2008, 70 : 1005 - 1027
  • [40] Gaussian graphical models with applications to omics analyses
    Shutta, Katherine H.
    De Vito, Roberta
    Scholtens, Denise M.
    Balasubramanian, Raji
    STATISTICS IN MEDICINE, 2022, 41 (25) : 5150 - 5187