Abstract

Recent work on the method of moments enable consistent parameter estimation, but only for certain types of latent-variable models. On the other hand, pure likelihood objectives, though more universally applicable, are difficult to optimize. In this work, we show that using the method of moments in conjunction with composite likelihood yields consistent parameter estimates for a much broader class of discrete directed and undirected graphical models, including loopy graphs with high treewidth. Specifically, we use tensor factorization to reveal information about the hidden variables. This allows us to construct convex likelihoods which can be globally optimized to recover the parameters.