Closure properties of uniform convergence of empirical means and PAC learnability under a family of probability measures

Document Type

Article

Publication Date

8-1-2001

Abstract

Open Problem No. 12.2 of (Vidyasagar, A Theory of Learning and Generalization: with Application to Neural Networks and Control Systems, Springer, London, 1997) asks: "Are the properties of uniform convergence of empirical means, and learnability preserved when the family of probability measures is replaced by its closure?" In this note, the question is answered in the affirmative. Further, it is shown that these properties are not preserved in general if the family of probability measures is replaced by its convex closure. An open question is posed as to whether it is possible to replace the family of probability measures by its convex closure in case the family is compact. © 2001 Elsevier Science B.V. All rights reserved.

Identifier

0034910132 (Scopus)

Publication Title

Systems and Control Letters

External Full Text Location

https://doi.org/10.1016/S0167-6911(00)00086-4

ISSN

01676911

First Page

151

Last Page

157

Issue

2

Volume

42

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