Asymptotic analysis of Bayesian generalization error with Newton diagram

Statistical learning machines that have singularities in the parameter space, such as hidden Markov models, Bayesian networks, and neural networks, are widely used in the field of information engineering. Singularities in the parameter space determine the accuracy of estimation in the Bayesian scena...

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Bibliographic Details
Published in:Neural networks 2010, Vol.23 (1), p.35-43
Main Authors: Yamazaki, Keisuke, Aoyagi, Miki, Watanabe, Sumio
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Automatic Data Processing
Bayes generalization error
Bayes Theorem
Computer science
control theory
systems
Computer Simulation
Connectionism. Neural networks
Exact sciences and technology
Generalization (Psychology)
Humans
Information Storage and Retrieval
Newton diagram
Statistical singular models
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Summary:Statistical learning machines that have singularities in the parameter space, such as hidden Markov models, Bayesian networks, and neural networks, are widely used in the field of information engineering. Singularities in the parameter space determine the accuracy of estimation in the Bayesian scenario. The Newton diagram in algebraic geometry is recognized as an effective method by which to investigate a singularity. The present paper proposes a new technique to plug the diagram in the Bayesian analysis. The proposed technique allows the generalization error to be clarified and provides a foundation for an efficient model selection. We apply the proposed technique to mixtures of binomial distributions.
ISSN:0893-6080
1879-2782
DOI:10.1016/j.neunet.2009.07.029