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Learning Parities in the Mistake-Bound model

Authors: Harry Buhrman, David Garcia-Soriano, and Arie Matsliah

Published in: Dagstuhl Seminar Proceedings, Volume 9421, Algebraic Methods in Computational Complexity (2010)

Abstract

We study the problem of learning parity functions that depend on at most $k$ variables ($k$-parities) attribute-efficiently in the mistake-bound model. We design a simple, deterministic, polynomial-time algorithm for learning $k$-parities with mistake bound $O(n^{1-frac{c}{k}})$, for any constant $c > 0$. This is the first polynomial-time algorithms that learns $omega(1)$-parities in the mistake-bound model with mistake bound $o(n)$. Using the standard conversion techniques from the mistake-bound model to the PAC model, our algorithm can also be used for learning $k$-parities in the PAC model. In particular, this implies a slight improvement on the results of Klivans and Servedio cite{rocco} for learning $k$-parities in the PAC model. We also show that the $widetilde{O}(n^{k/2})$ time algorithm from cite{rocco} that PAC-learns $k$-parities with optimal sample complexity can be extended to the mistake-bound model.

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Harry Buhrman, David Garcia-Soriano, and Arie Matsliah. Learning Parities in the Mistake-Bound model. In Algebraic Methods in Computational Complexity. Dagstuhl Seminar Proceedings, Volume 9421, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{buhrman_et_al:DagSemProc.09421.5,
  author =	{Buhrman, Harry and Garcia-Soriano, David and Matsliah, Arie},
  title =	{{Learning Parities in the Mistake-Bound model}},
  booktitle =	{Algebraic Methods in Computational Complexity},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9421},
  editor =	{Manindra Agrawal and Lance Fortnow and Thomas Thierauf and Christopher Umans},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09421.5},
  URN =		{urn:nbn:de:0030-drops-24178},
  doi =		{10.4230/DagSemProc.09421.5},
  annote =	{Keywords: Attribute-efficient learning, parities, mistake-bound}
}

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Learning Parities in the Mistake-Bound model

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