Asymptotic analysis of Bayesian generalization error with Newton diagram

DOI10.1016/J.NEUNET.2009.07.029zbMath1396.68108DBLPjournals/nn/YamazakiAW10OpenAlexW2094838356WikidataQ44770124 ScholiaQ44770124MaRDI QIDQ1784534

Miki Aoyagi, Keisuke Yamazaki, Sumio Watanabe

Publication date: 27 September 2018

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.neunet.2009.07.029

zbMATH Keywords

Newton diagramBayes generalization errorstatistical singular models

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05)

Related Items (9)

Consideration on singularities in learning theory and the learning coefficient ⋮ Learning Coefficient of Generalization Error in Bayesian Estimation and Vandermonde Matrix-Type Singularity ⋮ Bayesian estimation of multidimensional latent variables and its asymptotic accuracy ⋮ Recent advances in algebraic geometry and Bayesian statistics ⋮ An alternative view of variational Bayes and asymptotic approximations of free energy ⋮ On equivalent parameter learning in simplified feature space based on Bayesian asymptotic analysis ⋮ Comparing two Bayes methods based on the free energy functions in Bernoulli mixtures ⋮ A Bayesian Learning Coefficient of Generalization Error and Vandermonde Matrix-Type Singularities ⋮ Asymptotic accuracy of Bayes estimation for latent variables with redundancy

Cites Work

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• Stochastic complexity and modeling
• Estimating the dimension of a model
• Singularities in mixture models and upper bounds of stochastic complexity.
• Stochastic complexities of reduced rank regression in Bayesian estimation
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Algebraic Analysis for Nonidentifiable Learning Machines
• On the Problem in Model Selection of Neural Network Regression in Overrealizable Scenario
• Variational Bayes Solution of Linear Neural Networks and Its Generalization Performance
• Testing in locally conic models, and application to mixture models
• A decision-theoretic extension of stochastic complexity and its applications to learning
• Computation and applications of the Newton polyhedrons

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