Estimation of Undirected Graph with Finite Mixture of Nonparanormal Distribution

Abstract

In this paper, the nonparanormal graphical mixture model is introduced as a flexible multivariate analysis tool with a semiparametric approach. In this model, mixture component densities are nonparanormal distributions with different covariance matrices. Therefore, each mixture component may have a different dependency structure with the probability of the respective mixture proportion. Our suggested estimation algorithm uses expectation maximization algorithm for maximization of $$\ell _1$$ -regularized likelihood function. Graphical lasso algorithm and extended Bayesian information criterion are used in each iteration of the EM algorithm for the model selection purposes. Simulation studies show that the proposed method performs better than the alternative Gaussian graphical mixture model, especially for non-Gaussian heterogeneous data. The proposed method is also applied to water-level dataset and is compared with the results of Gaussian mixture model.