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Abstract: We examine the relationship between the VC-dimension and the number of parameters of a smoothly parametrized function class. We show that the VCdimension of such a function class is at least k if there exists a k-dimensional differentiable manifold in the parameter space such that each member of the manifold corresponds to a different decision boundary. Using this result, we are able to obtain lower bounds on the VC-dimension proportional to the number of parameters for several function classes ... (Update)
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BibTeX entry: (Update)
@inproceedings{ lee94lower,
author = "Wee Sun Lee and Peter L. Bartlett and Robert C. Williamson",
title = "Lower Bounds on the {VC}-Dimension of Smoothly Parametrized Function Classes",
booktitle = "Computational Learing Theory",
pages = "362-367",
year = "1994",
url = "citeseer.ist.psu.edu/122125.html" }
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