Bayesian invariant measurements of generalisation for continuous distributions

Zhu, Huaiyu and Rohwer, Richard (1995). Bayesian invariant measurements of generalisation for continuous distributions. Technical Report. Aston University, Birmingham B4 7ET, UK.

Abstract

A family of measurements of generalisation is proposed for estimators of continuous distributions. In particular, they apply to neural network learning rules associated with continuous neural networks. The optimal estimators (learning rules) in this sense are Bayesian decision methods with information divergence as loss function. The Bayesian framework guarantees internal coherence of such measurements, while the information geometric loss function guarantees invariance. The theoretical solution for the optimal estimator is derived by a variational method. It is applied to the family of Gaussian distributions and the implications are discussed. This is one in a series of technical reports on this topic; it generalises the results of ¸iteZhu95:prob.discrete to continuous distributions and serve as a concrete example of a larger picture ¸iteZhu95:generalisation.

Divisions: ?? 13770100JJ ??
Uncontrolled Keywords: neural network,Bayesian decision method,geometric loss function,optimal estimator,Gaussian distributions
Published Date: 1995

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