An improved Hara-Takamura procedure by sharing computations on junction tree in Gaussian graphical models

Authors:
Ping-Feng Xu;Jianhua Guo;Man-Lai Tang
Affiliations:
School of Mathematics and Statistics, Northeast Normal University, Changchun, China 130024 and School of Basic Science, Changchun University of Technology, Changchun, China 130012;Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun, China 130024;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, China
Venue:
Statistics and Computing
Year:
2012

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Abstract

In this paper, we propose an improved iterative proportional scaling procedure for maximum likelihood estimation for multivariate Gaussian graphical models. Our proposed procedure allows us to share computations when adjusting different clique marginals on junction trees. This makes our procedure more efficient than existing procedures for maximum likelihood estimation for multivariate Gaussian graphical models. Some numerical experiments are conducted to illustrate the efficiency of our proposed procedure for maximum likelihood estimation of Gaussian graphical models with the number of variables up to the two thousands. We also demonstrate our proposed procedures by two genetic examples.