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Beyond prediction: A framework for inference with variational approximations in mixture models.

T Westling1, T H McCormick2

  • 1Center for Causal Inference, University of Pennsylvania.

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|July 28, 2020
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Summary
This summary is machine-generated.

This study establishes theoretical properties for variational inference estimators in complex models. It provides conditions for consistency and asymptotic normality, enhancing statistical inference capabilities.

Keywords:
generalized linear mixed modelsprofile M-estimation

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Area of Science:

  • Statistics
  • Computational Biology
  • Biostatistics

Background:

  • Variational inference is widely used for parameter estimation in hierarchical and mixed models across health, social, and biological sciences.
  • It approximates intractable distributions to optimize a lower bound on the log-likelihood, enabling efficient fitting of complex models to large datasets.
  • However, the theoretical properties of variational estimators are not well understood, limiting their inferential applications.

Purpose of the Study:

  • To establish theoretical properties for estimators derived from variational inference.
  • To connect variational inference to profile M-estimation to derive conditions for consistency and asymptotic normality.
  • To motivate methodological improvements for variational inference.

Main Methods:

  • Connecting variational inference estimators to profile M-estimation.
  • Deriving regularity conditions for consistency and asymptotic normality.
  • Developing methods for estimating the asymptotic model-robust covariance matrix and a one-step correction for efficiency.
  • Evaluating methods via simulation studies and real-world data analysis.

Main Results:

  • Established theoretical foundations for variational inference estimators, linking them to profile M-estimation.
  • Provided conditions ensuring consistency and asymptotic normality of these estimators.
  • Motivated and developed three practical improvements: robust covariance estimation, an efficiency-enhancing one-step correction, and consistency assessment.

Conclusions:

  • The theoretical framework provides crucial understanding of variational inference estimators' behavior.
  • Methodological improvements enhance the reliability and efficiency of variational inference in practice.
  • Findings support broader adoption of variational inference for robust statistical inference in large-scale scientific studies.