Resolution of Singularities and Stochastic Complexity of Complete Bipartite Graph-Type Spin Model in Bayesian Estimation

Authors:
Miki Aoyagi;Sumio Watanabe
Affiliations:
Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuda, Midori-ku, R2-5, Yokohama, 226-8503, Japan;Precision and Intelligence Laboratory, Tokyo Institute of Technology, 4259 Nagatsuda, Midori-ku, R2-5, Yokohama, 226-8503, Japan
Venue:
MDAI '07 Proceedings of the 4th international conference on Modeling Decisions for Artificial Intelligence
Year:
2007

Citing 4
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Abstract

In this paper, we obtain the main term of the average stochastic complexity for certain complete bipartite graph-type spin models in Bayesian estimation. We study the Kullback function of the spin model by using a new method of eigenvalue analysis first and use a recursive blowing up process for obtaining the maximum pole of the zeta function which is defined by using the Kullback function. The papers [1,2] showed that the maximum pole of the zeta function gives the main term of the average stochastic complexity of the hierarchical learning model.