Graphical models are commonly used tools for modeling multivariate random
variables. While there exist many convenient multivariate distributions such as
Gaussian distribution for continuous data, mixed data with the presence of
discrete variables or a combination of both continuous and discrete variables
poses new challenges in statistical modeling. In this paper, we propose a
semiparametric model named latent Gaussian copula model for binary and mixed
data. The observed binary data are assumed to be obtained by dichotomizing a
latent variable satisfying the Gaussian copula distribution or the
nonparanormal distribution. The latent Gaussian model with the assumption that
the latent variables are multivariate Gaussian is a special case of the
proposed model. A novel rank-based approach is proposed for both latent graph
estimation and latent principal component analysis. Theoretically, the proposed
methods achieve the same rates of convergence for both precision matrix
estimation and eigenvector estimation, as if the latent variables were
observed. Under similar conditions, the consistency of graph structure recovery
and feature selection for leading eigenvectors is established. The performance
of the proposed methods is numerically assessed through simulation studies, and
the usage of our methods is illustrated by a genetic dataset.

本文提出了一种名为潜在高斯 Copula 模型的半参数模型，用于建模二元和混合数据的多元统计学习。