Folded Concave Penalized Estimation of Conditional Copula Graphical Models with Application to Microbial Networks

• Activity Number: 487 - Neural Networks, Deep Learning, and RKHS
• Type: Contributed
• Date/Time: Wednesday, August 1, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Bingyuan Liu* and Lingzhou Xue
• Companies: Pennsylvania State University and Penn State University and National Institute of Statistical Sciences
• Keywords: conditional graphical model; Semiparametric copula model; Nonconvex optimization; Reproducing kernel Hilbert space; Microbiome network; Oracle Property

Abstract

A sparse precision matrix estimation is desirable in constructing sparse Gaussian graphical models. In genome and microbiome study, the conditional Gaussian graphical model is proposed to solve the case when considering the effect of other dependent variables when learning graphical models. There is still no existing method which could deal with the case when normality assumption does not hold in the conditional Graphical model. In this paper, we introduce a novel conditional copula graphical model. To efficiently learn the model, we first estimate the transformation function for each variable under semiparametric Gaussian copula assumption. Then we estimate the covariance matrix in RKHS, and finally estimate the folded concave penalized precision matrix based on covariance estimator. We establish the strong oracle property of our precision matrix estimation without requiring localization and incoherence. And we also propose an efficient algorithm to solve this type of nonconvex problem with numerical guarantees. We use simulation studies to illustrate the power of both our estimator and algorithm. We apply our method on microbiome network analysis conditioned on the host genetics.