High-Dimensional Mixed Graphical Model With Ordinal Data: Parameter Estimation And Statistical Inference

We consider parameter estimation and statistical inference of high-dimensional undirected graphical models for mixed data comprising both ordinal and continuous variables. We propose a flexible model called Latent Mixed Gaussian Copula Model that simultaneously deals with such mixed data by assuming that the observed ordinal variables are generated by latent variables. For parameter estimation, we introduce a convenient rank-based ensemble approach to estimate the latent correlation matrix, which can be subsequently applied to recover the latent graph structure. In addition, based on the ensemble estimator, we develop test statistics via a pseudolikelihood approach to quantify the uncertainty associated with the low dimensional components of high-dimensional parameters. Our theoretical analysis shows the consistency of the estimator and asymptotic normality of the test statistic. Experiments on simulated and real gene expression data are conducted to validate our approach.