In 1998, it was proved 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 compression 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 $\m{C}$, then $(X,\CC)$ 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.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/23133 |
| Date | January 2012 |
| Creators | Kalajdzievski, Damjan |
| Contributors | Pestov, Vladimir |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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