Copula Gaussian graphical models with hidden variables

Gaussian hidden variable graphical models are powerful tools to describe high-dimensional data; they capture dependencies between observed (Gaussian) variables by introducing a suitable number of hidden variables. However, such models are only applicable to Gaussian data. Moreover, they are sensitive to the choice of certain regularization parameters. In this paper, (1) copula Gaussian hidden variable graphical models are introduced, which extend Gaussian hidden variable graphical models to non-Gaussian data; (2) the sparsity pattern of the hidden variable graphical model is learned via stability selection, which leads to more stable results than cross-validation and other methods to select the regularization parameters. The proposed methods are validated on synthetic and real data.