Measurability Aspects of the Compactness Theorem for Sample Compression Schemes
Abstract
It was proved in 1998 by Ben-David and Litman that a concept space has a sample compression scheme of size d if and only if every finite subspace has a sample compression scheme of size d. In the compactness theorem, measurability of the hypotheses of the created sample compression scheme is not guaranteed; at the same time measurability of the hypotheses is a necessary condition for learnability. In this thesis we discuss when a sample compression scheme, created from com- pression schemes on finite subspaces via the compactness theorem, have measurable hypotheses. We show that if X is a standard Borel space with a d-maximum and universally separable concept class C, then (X,C) has a sample compression scheme of size d with universally Borel measurable hypotheses. Additionally we introduce a new variant of compression scheme called a copy sample compression scheme.
Cite
@article{arxiv.1205.5819,
title = {Measurability Aspects of the Compactness Theorem for Sample Compression Schemes},
author = {Damjan Kalajdzievski},
journal= {arXiv preprint arXiv:1205.5819},
year = {2015}
}
Comments
Latex 2e, 64 pages, 1 figure. This is an M.Sc. thesis defended on July 4'th 2012 at the University of Ottawa, Canada, under the supervision of Dr. V. Pestov, and with examiners Dr. J. Levy and Dr. S. Zilles