Fast Moment Estimation for Generalized Latent Dirichlet Models

Area of Science:

• Statistics
• Machine Learning
• Computational Statistics

Background:

• Dirichlet latent variable models are widely used for analyzing data with complex structures.
• Traditional parameter estimation methods like Expectation-Maximization (EM), Variational Inference (VI), and Markov Chain Monte Carlo (MCMC) can be computationally intensive and sensitive to distributional assumptions.

Purpose of the Study:

• To develop a novel, computationally efficient, and statistically robust method for parameter estimation in Dirichlet latent variable models.
• To address challenges associated with mixed data types within these models.

Main Methods:

• A generalized method of moments (GMM) approach is proposed for parameter estimation.
• The method, named Moment Estimation for latent Dirichlet models (MELD), derives population moment conditions by marginalizing out sample-specific latent variables.
• Parameter estimation does not require instantiation of latent variables and is agnostic to observation distributional assumptions.

Main Results:

• MELD demonstrates computational and statistical advantages over alternative estimation methods.
• Performance is robust across different distributional assumptions of the observed data.
• Simulations and real-world dataset applications show the efficacy and promise of the MELD approach.

Conclusions:

• MELD provides a fast and flexible alternative for parameter estimation in Dirichlet latent variable models.
• The method's ability to handle mixed data types and its computational efficiency make it suitable for large-scale applications.
• Further research can explore extensions of MELD to more complex latent variable models.