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Asymptotic accuracy of Bayesian estimation for a single latent variable.

Keisuke Yamazaki1

  • 1Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, G5-19 4259 Nagatsuta, Midori-ku, Yokohama, Japan.

Neural Networks : the Official Journal of the International Neural Network Society
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Summary

Bayes estimation for single latent variables in machine learning is as accurate as maximum-likelihood estimation. The Bayes method shows advantages only for joint, multivariable estimations in hierarchical parametric models.

Keywords:
Bayes estimationHierarchical parametric modelsLatent variableUnsupervised learning

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Area of Science:

  • Data Science
  • Machine Learning
  • Statistical Modeling

Background:

  • Hierarchical parametric models, like mixture models, are crucial in data science and machine learning.
  • These models utilize observable and latent variables, with less theoretical analysis on latent variable estimation accuracy.
  • Previous work established Bayes estimation's superiority for joint latent variable probabilities.

Purpose of the Study:

  • To investigate the asymptotic accuracy of Bayes estimation for single latent variables.
  • To compare the performance of Bayes and maximum-likelihood methods for single latent variable estimation.
  • To determine conditions under which Bayes estimation offers advantages.

Main Methods:

  • Derivation of asymptotic expansions for error functions using Kullback-Leibler divergence.
  • Analysis conducted under conditions of statistical regularity.
  • Focus on two types of single-variable estimations.

Main Results:

  • The asymptotic accuracies of Bayes and maximum-likelihood methods for single latent variable estimation are equivalent.
  • The Bayes method's advantage is limited to multivariable estimations.
  • Error functions were analyzed using asymptotic expansions.

Conclusions:

  • For single latent variable estimation in hierarchical models, Bayes and maximum-likelihood methods offer similar asymptotic accuracy.
  • The theoretical advantage of the Bayes method is primarily in joint or multivariable estimations.
  • This study clarifies the scope of Bayes estimation's benefits in machine learning models.