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Published in:
Chervonenkis’s Recollections Read chapter Read first chapter

2015 | OriginalPaper | Chapter

14. Classes of Functions Related to VC Properties

Author : R. M. Dudley

Published in: Measures of Complexity

Publisher: Springer International Publishing

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Abstract

The notion of Vapnik–Chervonenkis (VC) class of sets can be extended to classes of functions in a few ways. Under further hypotheses, central limit theorems for empirical measures can be proved uniformly over such classes. Specific such classes on Euclidean spaces can be used to show the existence of location vector and scatter matrix functionals, replacing mean vectors and covariance matrices, but on classes of probability measures P that are weakly dense, weakly open, and so contain arbitrarily heavy-tailed distributions.

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previous chapter Measures of Complexity in the Theory of Machine Learning
next chapter On Martingale Extensions of Vapnik–Chervonenkis Theory with Applications to Online Learning
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Metadata
Title
Classes of Functions Related to VC Properties
Author
R. M. Dudley
Copyright Year
2015
Book
Measures of Complexity

Print ISBN: 978-3-319-21851-9

Electronic ISBN: 978-3-319-21852-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-21852-6_14

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