Fast moment estimation for generalized latent Dirichlet models

We develop a generalized method of moments (GMM) approach for fast parameter estimation in a new class of Dirichlet latent variable models with mixed data types. Parameter estimation via GMM has been demonstrated to have computational and statistical advantages over alternative methods, such as expectation maximization, variational inference, and Markov chain Monte Carlo. The key computational advantage of our method (MELD) is that parameter estimation does not require instantiation of the latent variables. Moreover, a representational advantage of the GMM approach is that the behavior of the model is agnostic to distributional assumptions of the observations. We derive population moment conditions after marginalizing out the sample-specific Dirichlet latent variables. The moment conditions only depend on component mean parameters. We illustrate the utility of our approach on simulated data, comparing results from MELD to alternative methods, and we show the promise of our approach through the application of MELD to several data sets.