  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 advan- tage 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.
