A note on sample complexity of learning binary output neural networks under fixed input distributions

Details A note on sample complexity of learning binary output neural networks under fixed input distributions A note on sample complexity of learning binary output neural networks under fixed input distributions

2010-07-08

arxiv.org/abs/1007.1282v1

Proc. 2010 Eleventh Brazilian Symposium on Neural Networks (S\~ao Bernardo do Campo, SP, Brazil, 23-28 October 2010), IEEE Com

Computer Science

Learning

6 pages, latex in IEEE conference proceedings format

Scientific paper

We show that the learning sample complexity of a sigmoidal neural network constructed by Sontag (1992) required to achieve a given misclassification error under a fixed purely atomic distribution can grow arbitrarily fast: for any prescribed rate of growth there is an input distribution having this rate as the sample complexity, and the bound is asymptotically tight. The rate can be superexponential, a non-recursive function, etc. We further observe that Sontag's ANN is not Glivenko-Cantelli under any input distribution having a non-atomic part.

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