title: On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis.
abstract: 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.
authors.affiliation: Professor of Statistics, The Pennsylvania State University, 326 Thomas Building, University Park, PA 16802.
authors.forename: Bing
authors.initials: B
authors.lastname: Li
authors.affiliation: Assistant Professor of Statistics, Purdue University, 250 N. University Street, West Lafayette, IN 47907.
authors.forename: Hyonho
authors.initials: H
authors.lastname: Chun
authors.affiliation: Professor of Biostatistics, Yale University, Suite 503, 300 George Street, New Haven, CT 06410.
authors.forename: Hongyu
authors.initials: H
authors.lastname: Zhao
keywords: Additive conditional independence; additive precision operator; conditional independence; copula; covariance operator; gaussian graphical model; nonparanormal graphical model; reproducing kernel Hilbert space