Fast Moment Estimation for Generalized Latent Dirichlet Models

ABSTRACT

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 computational and statistical advantages over alternative methods, such as expectation maximization, variational inference, and Markov chain Monte Carlo. A key computational advantage of our method, Moment Estimation for latent Dirichlet models (MELD), is that parameter estimation does not require instantiation of the latent variables. Moreover, performance 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 to several datasets. Supplementary materials for this article are available online.

KEYWORDS:

• Generalized method of moments
• Latent Dirichlet allocation
• Latent variables
• Mixed membership model
• Mixed scale data
• Tensor factorization

Supplementary Materials

We provide supplementary materials that include (a) derivations of asymptotic optimal weight matrices; (b) calculation of MSE and computational complexity analysis; (c) two additional simulations with categorical variables and mixed data types; (d) Supplementary Tables S1– S25; (e) Supplementary Figures S1– S10. Python code implementing MELD and code used to generate results in the article are available at https://github.com/judyboon/MELD.