IJPAM: Volume 52, No. 2 (2009)

LOG CANONICAL THRESHOLD OF VANDERMONDE
MATRIX TYPE SINGULARITIES AND GENERALIZATION
ERROR OF A THREE-LAYERED NEURAL NETWORK
IN BAYESIAN ESTIMATION

Miki Aoyagi
Advanced Research Institute for the Sciences and Humanities
Nihon University
Nihon University Kaikan Daini Bekkan
12-5, Goban-cho, Chiyoda-ku, Tokyo 102-8251, JAPAN
e-mail: [email protected]


Abstract.The log canonical threshold of Vandermonde matrix type singularities over the real number field serves to measure the learning efficiencies in hierarchical learning models. Imposing certain orthogonality conditions for such singularities, explicit computational results for the log canonical thresholds are given. In applying such results to a three-layered neural network, we are able to clarify its generalization error and its stochastic complexity found useful in learning theory.

Received: March 2, 2009

AMS Subject Classification: 32S10, 14Q15, 62D05, 62M20, 62M45

Key Words and Phrases: log canonical threshold, zeta function, resolution of singularities, generalization error, layered neural networks

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 2