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Fast Moment Estimation for Generalized Latent Dirichlet Models.

Shiwen Zhao1, Barbara E Engelhardt2, Sayan Mukherjee1

  • 1Department of Statistical Science, Duke University, Durham, NC.

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|July 25, 2022
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Summary
This summary is machine-generated.

We introduce Moment Estimation for latent Dirichlet models (MELD), a fast generalized method of moments approach for parameter estimation in Dirichlet latent variable models. MELD offers computational and statistical advantages over other methods for mixed data types.

Keywords:
Generalized method of momentsLatent Dirichlet allocationLatent variablesMixed membership modelMixed scale dataTensor factorization

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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.