Consistent inference of probabilities in layered networks: Predictions and generalization

Naftali Tishby*, Esther Levin, Sara A. Solla

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

112 Scopus citations


The problem of learning a general input-output relation using a layered neural network is discussed in a statistical framework. By imposing the consistency condition that the error minimization be equivalent to a likelihood maximization for training the network, the authors arrive at a Gibbs distribution on a canonical ensemble of networks with the same architecture. This statistical description enables them to evaluate the probability of a correct prediction of an independent example, after training the network on a given training set. The prediction probability is highly correlated with the generalization ability of the network, as measured outside the training set. This suggests a general and practical criterion for training layered networks by minimizing prediction errors. The authors demonstrate the utility of this criterion for selecting the optimal architecture in the continuity problem. As a theoretical application of the statistical formalism, they discuss the question of learning curves and estimate the sufficient training size needed for correct generalization, in a simple example.

Original languageEnglish (US)
Title of host publicationIJCNN Int Jt Conf Neural Network
Editors Anon
PublisherPubl by IEEE
Number of pages7
StatePublished - Dec 1 1989
EventIJCNN International Joint Conference on Neural Networks - Washington, DC, USA
Duration: Jun 18 1989Jun 22 1989


OtherIJCNN International Joint Conference on Neural Networks
CityWashington, DC, USA

ASJC Scopus subject areas

  • General Engineering


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