  The Gaussian graphical model is a widely used tool for learning gene
regulatory networks with high-dimensional gene expression data. Most existing
methods for Gaussian graphical models assume that the data are homogeneous,
i.e., all samples are drawn from a single Gaussian distribution. However, for
many real problems, the data are heterogeneous, which may contain some
subgroups or come from different resources. This paper proposes to model the
heterogeneous data using a mixture Gaussian graphical model, and apply the
imputation-consistency algorithm, combining with the $\psi$-learning algorithm,
to estimate the parameters of the mixture model and cluster the samples to
different subgroups. An integrated Gaussian graphical network is learned across
the subgroups along with the iterations of the imputation-consistency
algorithm. The proposed method is compared with an existing method for learning
mixture Gaussian graphical models as well as a few other methods developed for
homogeneous data, such as graphical Lasso, nodewise regression and
$\psi$-learning. The numerical results indicate superiority of the proposed
method in all aspects of parameter estimation, cluster identification and
network construction. The numerical results also indicate generality of the
proposed method: it can be applied to homogeneous data without significant
harms.
