Learning Unions of $ω(1)$-Dimensional Rectangles

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dc.creatorAtici, Alp
dc.creatorServedio, Rocco A.
dc.date2005-10-14
dc.date2007-06-26
dc.date.accessioned2026-07-07T10:02:19Z
dc.date.available2026-07-07T10:02:19Z
dc.descriptionWe consider the problem of learning unions of rectangles over the domain $[b]^n$, in the uniform distribution membership query learning setting, where both b and n are "large". We obtain poly$(n, \log b)$-time algorithms for the following classes: - poly$(n \log b)$-way Majority of $O(\frac{\log(n \log b)} {\log \log(n \log b)})$-dimensional rectangles. - Union of poly$(\log(n \log b))$ many $O(\frac{\log^2 (n \log b)} {(\log \log(n \log b) \log \log \log (n \log b))^2})$-dimensional rectangles. - poly$(n \log b)$-way Majority of poly$(n \log b)$-Or of disjoint $O(\frac{\log(n \log b)} {\log \log(n \log b)})$-dimensional rectangles. Our main algorithmic tool is an extension of Jackson's boosting- and Fourier-based Harmonic Sieve algorithm [Jackson 1997] to the domain $[b]^n$, building on work of [Akavia, Goldwasser, Safra 2003]. Other ingredients used to obtain the results stated above are techniques from exact learning [Beimel, Kushilevitz 1998] and ideas from recent work on learning augmented $AC^{0}$ circuits [Jackson, Klivans, Servedio 2002] and on representing Boolean functions as thresholds of parities [Klivans, Servedio 2001].
dc.description25 pages. Some corrections. Recipient of E. M. Gold award ALT 2006. To appear in Journal of Theoretical Computer Science
dc.identifierhttps://arxiv.org/abs/cs/0510038
dc.identifierhttp://arxiv.org/abs/cs/0510038
dc.identifierTheoretical Computer Science, Vol. 405, No. 3, 209--222 (2008)
dc.identifierdoi:10.1016/j.tcs.2008.06.036
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168935
dc.subjectMachine Learning
dc.subjectF.2.2; I.2.6
dc.titleLearning Unions of $ω(1)$-Dimensional Rectangles
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