Undirected graphical models are a popular class of statistical models, used in
a
wide variety of applications. In many settings, however, it might not be clear
which subclass of graphical models to use, particularly for non-Gaussian and
non-categorical data. In this paper, we consider a general sub-class of
graphical models where the node-wise conditional distributions arise from
exponential families. This allows us to derive multivariate graphical model
distributions from univariate exponential family distributions, such as the
Poisson, negative binomial, and exponential distributions. Our key
contributions
include a class of $M$-estimators to fit these graphical model distributions;
and
rigorous sparsistency analysis for these $M$-estimators.