Estimating Latent-Variable Graphical Models using Moments and Likelihoods

Recent work in method of moments provide consistent estimates for latent-variable models, avoiding local optima issues, but these methods can only be applied to certain types of graphical models. In this work, we show that the method of moments in conjunction with a composite marginal likelihood objective yields consistent parameter estimates for a much broader class of directed and undirected graphical models, including loopy graphs with high treewidth. Specifically, we use tensor factorization to reveal partial information about the hidden variables, rendering the otherwise non-convex negative log-likelihood convex. Our approach gracefully extends to models outside our class by incorporating the partial information via posterior regulraization.