  Fitting a graphical model to a collection of random variables given sample
observations is a challenging task if the observed variables are influenced by
latent variables, which can induce significant confounding statistical
dependencies among the observed variables. We present a new convex relaxation
framework based on regularized conditional likelihood for latent-variable
graphical modeling in which the conditional distribution of the observed
variables conditioned on the latent variables is given by an exponential family
graphical model. In comparison to previously proposed tractable methods that
proceed by characterizing the marginal distribution of the observed variables,
our approach is applicable in a broader range of settings as it does not
require knowledge about the specific form of distribution of the latent
variables and it can be specialized to yield tractable approaches to problems
in which the observed data are not well-modeled as Gaussian. We demonstrate the
utility and flexibility of our framework via a series of numerical experiments
on synthetic as well as real data.
