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In this article, we consider the problem of reconstructing networks forcontinuous, binary, count and discrete ordinal variables by estimating sparseprecision matrix in Gaussian copula graphical models. We propose twoapproaches: $\ell_1$ penalized extended rank likelihood with Monte CarloExpectation-Maximization algorithm (copula EM glasso) and copula skeptic withpair-wise copula estimation for copula Gaussian graphical models. The proposedapproaches help to infer networks arising from nonnormal and mixed variables.We demonstrate the performance of our methods through simulation studies andanalysis of breast cancer genomic and clinical data and maize genetics data.

Penalized EM algorithm and copula skeptic graphical models for inferring networks for mixed variables