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Activity Number: 48
Type: Invited
Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract - #310463
Title: On an Additive Semi-Graphoid Model for Statistical Networks with Application to Pathway Analysis
Author(s): Bing Li*+ and Hyonho Chun and Hongyu Zhao
Companies: The Pennsylvania State University and Purdue University and Yale University
Keywords: Additive conditional independence ; additive precision operator ; copula ; gaussian graphical model ; nonparanormal graphical model ; reproducing kernel Hilbert space
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.


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