On a singular point to contribute to a learning coefficient and weighted resolution of singularities

Authors:
Takeshi Matsuda;Sumio Watanabe
Affiliations:
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Kanagawa, Japan;Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama, Kanagawa, Japan
Venue:
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Year:
2007

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ICANN'06 Proceedings of the 16th international conference on Artificial Neural Networks - Volume Part I

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Abstract

A lot of learning machines which have the hidden variables or the hierarchical structures are the singular statistical models. They have a different learning performance from the regular statistical models. In this paper, we show that the learning coefficient is easily computed by weighted blow up, in contrast, and that there is the case that the learning coefficient cannot be correctly computed by blowing up at the origin O only.