Consideration on Singularities in Learning Theory and the Learning Coefficient
Author:
Open Access
- 6 September 2013
- Vol. 15 (9) , 3714-3733
Abstract
We consider the learning coefficients in learning theory and give two new methods for obtaining these coefficients in a homogeneous case: a method for finding a deepest singular point and a method to add variables. In application to Vandermonde matrix-type singularities, we show that these methods are effective. The learning coefficient of the generalization error in Bayesian estimation serves to measure the learning efficiency in singular learning models. Mathematically, the learning coefficient corresponds to a real log canonical threshold of singularities for the Kullback functions (relative entropy) in learning theory.Keywords
This publication has 18 references indexed in Scilit:
- Learning Coefficient of Generalization Error in Bayesian Estimation and Vandermonde Matrix-Type SingularityNeural Computation, 2012
- Asymptotic analysis of Bayesian generalization error with Newton diagramNeural Networks, 2010
- Stochastic complexities of reduced rank regression in Bayesian estimationNeural Networks, 2005
- Singularities of pairs via jet schemesJournal of the American Mathematical Society, 2002
- Algebraic geometrical methods for hierarchical learning machinesNeural Networks, 2001
- Algebraic Analysis for Nonidentifiable Learning MachinesNeural Computation, 2001
- Singularities of pairs1997
- A Regularity Condition of the Information Matrix of a Multilayer Perceptron NetworkNeural Networks, 1996
- Uniqueness of the weights for minimal feedforward nets with a given input-output mapNeural Networks, 1992
- A new look at the statistical model identificationIEEE Transactions on Automatic Control, 1974