High dimensional semiparametric latent graphical model for mixed data

• 成果类型: Article
• 署名作者: Fan, Jianqing; Liu, Han; Ning, Yang; Zou, Hui
• 署名单位: Princeton University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12168
• 发表日期: 2017
• 页码: 405-421
• 关键词: nonconcave penalized likelihood; variable selection; Matrix Estimation; arabidopsis-thaliana; gene network; SPARSE; minimization; regression; PATHWAY; Lasso

摘要

We propose a semiparametric latent Gaussian copula model for modelling mixed multivariate data, which contain a combination of both continuous and binary variables. The model assumes that the observed binary variables are obtained by dichotomizing latent variables that satisfy the Gaussian copula distribution. The goal is to infer the conditional independence relationship between the latent random variables, based on the observed mixed data. Our work has two main contributions: we propose a unified rank-based approach to estimate the correlation matrix of latent variables; we establish the concentration inequality of the proposed rank-based estimator. Consequently, our methods achieve the same rates of convergence for precision matrix estimation and graph recovery, as if the latent variables were observed. The methods proposed are numerically assessed through extensive simulation studies, and real data analysis.