Title: Inference of high-dimensional modified Poisson-type graphical models
Authors: Zhao Ren - University of Pittsburgh (United States) [presenting]
Abstract: The high dimensional graphical model has attracted great attention in biological network analysis with different types of omics data. To tailor the network analysis of important count-valued omics data, various Poisson-type graphical models were proposed, but the statistical inference of these models is not well studied. We investigate statistical inference of each edge for large modified Poisson-type graphical models. The key role in most existing inferential methods is played by a linear projection method to de-bias an initial regularized estimator. The major drawback of this approach in those non-Gaussian graphical models is that an extra sparsity assumption on the linear projection coefficient is required, which cannot be checked in practice. To solve this challenge, we first propose a novel estimator of each edge for Ising model via quadratic programming and show that our estimator is asymptotically normal without the above mentioned extra sparsity condition. In addition, we further show that whenever the extra sparsity condition is satisfied, our estimator is adaptively efficient and achieves the Fisher information. We then extend our approach to modified Poisson-type graphical models. The practical merit of the proposed method is demonstrated by an application to a novel RNA-seq gene expression data set in childhood atopic asthma in Puerto Ricans.