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Fitting a graphical model to a collection of random variables given sampleobservations is a challenging task if the observed variables are influenced bylatent variables, which can induce significant confounding statisticaldependencies among the observed variables. We present a new convex relaxationframework based on regularized conditional likelihood for latent-variablegraphical modeling in which the conditional distribution of the observedvariables conditioned on the latent variables is given by an exponential familygraphical model. In comparison to previously proposed tractable methods thatproceed by characterizing the marginal distribution of the observed variables,our approach is applicable in a broader range of settings as it does notrequire knowledge about the specific form of distribution of the latentvariables and it can be specialized to yield tractable approaches to problemsin which the observed data are not well-modeled as Gaussian. We demonstrate theutility and flexibility of our framework via a series of numerical experimentson synthetic as well as real data.

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