  Undirected graphical models have been especially popular for learning the
conditional independence structure among a large number of variables where the
observations are drawn independently and identically from the same
distribution. However, many modern statistical problems would involve
categorical data or time-varying data, which might follow different but related
underlying distributions. In order to learn a collection of related graphical
models simultaneously, various joint graphical models inducing sparsity in
graphs and similarity across graphs have been proposed. In this paper, we aim
to propose an implementable proximal point dual Newton algorithm (PPDNA) for
solving the group graphical Lasso model, which encourages a shared pattern of
sparsity across graphs. Though the group graphical Lasso regularizer is
non-polyhedral, the asymptotic superlinear convergence of our proposed method
PPDNA can be obtained by leveraging on the local Lipschitz continuity of the
Karush-Kuhn-Tucker solution mapping associated with the group graphical Lasso
model. A variety of numerical experiments on real data sets illustrates that
the PPDNA for solving the group graphical Lasso model can be highly efficient
and robust.
