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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects.

Marianne Menictas1, Gioia Di Credico2, Matt P Wand3

  • 1Harvard University.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|March 6, 2023
PubMed
Summary
This summary is machine-generated.

We developed streamlined algorithms for linear mixed models with crossed random effects. These methods offer accurate inference, balancing computational demands with varying levels of accuracy for different problem sizes.

Keywords:
Mean field variational BayesRasch analysisitem response theoryscalable statistical methodologysparse least squares systems

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Area of Science:

  • Statistics
  • Computational Statistics
  • Machine Learning

Background:

  • Linear mixed models (LMMs) are widely used in various scientific fields.
  • Fitting LMMs with crossed random effects, especially with large group dimensions, presents computational challenges.
  • Existing methods may struggle with scalability and efficiency in complex scenarios.

Purpose of the Study:

  • To derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects.
  • To address the computational bottlenecks associated with large group dimensions in LMMs.
  • To provide a comparative analysis of different variational inference strategies.

Main Methods:

  • Development of streamlined mean field variational Bayes algorithms.
  • Exploration of a hierarchy of relaxations for the mean field product restriction.
  • Implementation of sparse storage and computing alternatives.

Main Results:

  • The least stringent product restriction offers high inferential accuracy but requires significant computational resources.
  • Faster sparse alternatives provide computational efficiency at the cost of reduced inferential accuracy.
  • Algorithmic details and empirical results comparing three variational inference strategies are presented.

Conclusions:

  • The choice of variational inference strategy depends on the trade-off between inferential accuracy, storage, and computing resources.
  • Guidance is provided for users to select the optimal approach based on their specific problem size and available resources.
  • The derived algorithms offer practical solutions for fitting complex linear mixed models.