On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis

• 成果类型: Article
• 署名作者: Li, Bing; Chun, Hyonho; Zhao, Hongyu
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Purdue University System; Purdue University; Yale University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.882842
• 发表日期: 2014
• 页码: 1188-1204
• 关键词: conditional-independence; Dimension Reduction; variable selection; Lasso

摘要

We introduce a nonparametric method for estimating non-Gaussian graphical models based on a new statistical relation called additive conditional independence, which is a three-way relation among random vectors that resembles the logical structure of conditional independence. Additive conditional independence allows us to use one-dimensional kernel regardless of the dimension of the graph, which not only avoids the curse of dimensionality but also simplifies computation. It also gives rise to a parallel structure to the Gaussian graphical model that replaces the precision matrix by an additive precision operator. The estimators derived from additive conditional independence cover the recently introduced nonparanormal graphical model as a special case, but outperform it when the Gaussian copula assumption is violated. We compare the new method with existing ones by simulations and in genetic pathway analysis. Supplementary materials for this article are available online.