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Unsupervised estimation of latent variable models is a fundamental problemcentral to numerous applications of machine learning and statistics. This workpresents a principled approach for estimating broad classes of such models,including probabilistic topic models and latent linear Bayesian networks, usingonly second-order observed moments. The sufficient conditions foridentifiability of these models are primarily based on weak expansionconstraints on the topic-word matrix, for topic models, and on the directedacyclic graph, for Bayesian networks. Because no assumptions are made on thedistribution among the latent variables, the approach can handle arbitrarycorrelations among the topics or latent factors. In addition, a tractablelearning method via $\ell_1$ optimization is proposed and studied in numericalexperiments.

Learning Topic Models and Latent Bayesian Networks Under Expansion Constraints