Selection and estimation for mixed graphical models

• 成果类型: Article
• 署名作者: Chen, Shizhe; Witten, Daniela M.; Shojaie, Ali
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asu051
• 发表日期: 2015
• 页码: 4764
• 关键词: GENERALIZED LINEAR-MODELS; COVARIANCE ESTIMATION; variable selection; l(1)

摘要

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different exponential family form. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes whose conditional distributions take different parametric forms, and show that efficiency can be gained if edge estimates obtained from the regressions of particular nodes are used to reconstruct the graph. These results are illustrated with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies.