Abstract
A lot of learning machines which have hidden variables or hierarchical structures are singular statistical models. They have singular Fisher information matrices and different learning performance from regular statistical models. In this paper, we prove mathematically that the learning coefficient is determined by the analytic equivalence class of Kullback information, and show experimentally that the stochastic complexity by the MCMC method is also given by the equivalence class.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Arnol’d, V.I.: Normal forms of functions in neighbourhoods of degenerate critical points. Russian Mathematical Surveys 29(2), 10–50 (1974)
Aoyagi, M., Watanabe, S.: Stochastic complexities of reduced rank regression in Bayesian estimation. Neural Networks 18(7), 924–933 (2005)
Aoyagi, M., Watanabe, S.: Resolution of singularities and generalization error with Bayesian estimation for layered neural network. J88-D-II(10), 2112–2124 (2005)
Atiyah, M.F.: Resolution of singularities and division of distributions. Communications of Pure and Applied Mathematics 13, 145–150 (1970)
Watanabe, S.: Algebraic Analysis for Non-identifiable Learning Machines. Neural Computation 13(4), 899–933 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Matsuda, T., Watanabe, S. (2006). Analytic Equivalence of Bayes a Posteriori Distributions. In: Kollias, S.D., Stafylopatis, A., Duch, W., Oja, E. (eds) Artificial Neural Networks – ICANN 2006. ICANN 2006. Lecture Notes in Computer Science, vol 4131. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11840817_12
Download citation
DOI: https://doi.org/10.1007/11840817_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38625-4
Online ISBN: 978-3-540-38627-8
eBook Packages: Computer ScienceComputer Science (R0)