Learning Exponential Family Graphical Models with Latent Variables using Regularized Conditional Likelihood

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