Copula Gaussian graphical model for discrete data

Copula Gaussian graphical models are capable of describing dependencies between a large number of heterogeneous variables. In this paper, low-complexity algorithms are proposed for learning copula Gaussian graphical models from discrete data. The proposed approach is Monte-Carlo expectation maximization: in the E-step, an efficient Gibbs sampler is applied, and in the M-step, the sparse graphical model is inferred by solving a penalized maximize likelihood problem. The regularization parameter is determined through the BINCO method proposed by Li et al. Numerical results for both synthetic and real data demonstrate the effectiveness of the proposed approach.