Learning Parities in the Mistake-Bound model

Authors Harry Buhrman, David Garcia-Soriano, Arie Matsliah

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Harry Buhrman
David Garcia-Soriano
Arie Matsliah

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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)


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.
  • Attribute-efficient learning
  • parities
  • mistake-bound


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