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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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| Published in: | Neural networks 2010, Vol.23 (1), p.35-43 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c435t-ad60649be8d005237452869988b20874141ff065bc9ee11b48de539b622870793 |
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| cites | cdi_FETCH-LOGICAL-c435t-ad60649be8d005237452869988b20874141ff065bc9ee11b48de539b622870793 |
| container_end_page | 43 |
| container_issue | 1 |
| container_start_page | 35 |
| container_title | Neural networks |
| container_volume | 23 |
| creator | Yamazaki, Keisuke Aoyagi, Miki Watanabe, Sumio |
| description | 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. |
| doi_str_mv | 10.1016/j.neunet.2009.07.029 |
| format | article |
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| ispartof | Neural networks, 2010, Vol.23 (1), p.35-43 |
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| source | ScienceDirect Journals |
| 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 |
| title | Asymptotic analysis of Bayesian generalization error with Newton diagram |
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