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Generalization Performance of Bayes Optimal Classification Algorithm for Learning a Perceptron

Manfred OpperDavid Haussler

出版	Board of Studies in Computer and Information Sciences, University of California at Santa Cruz, 1991
URL	http://books.google.com.hk/books?id=GlZD0AEACAAJ&hl=&source=gbs_api

註釋

The generalization error of Bayes optimal classification algorithm when learning a perceptron from noise-free random training examples is calculated exactly using methods of statistical mechanics. It is shown that if an assumption of replica symmetry is made then, in the thermodynamic limit, the error of Bayes optimal algorithm is less than the error of a canonical stochastic learning algorithm, by a factor approaching √2 as the ratio of number of training examples to perceptron weights grows. In addition, it is shown that approximations to the generalization error of Bayes optimal algorithm can be achieved by learning algorithms that use a two layer neural net to learn a perceptron.