Learning parities in the mistake-bound model

  • Authors:
  • Harry Buhrman;David García-Soriano;Arie Matsliah

  • Affiliations:
  • CWI Amsterdam, Netherlands;CWI Amsterdam, Netherlands;CWI Amsterdam, Netherlands

  • Venue:
  • Information Processing Letters
  • Year:
  • 2010

Quantified Score

Hi-index 0.89

Visualization

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^-^1^k). This is the first polynomial-time algorithm to learn @w(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 over the results of Klivans and Servedio (2004) [1] for learning k-parities in the PAC model. We also show that the O@?(n^k^/^2) time algorithm from Klivans and Servedio (2004) [1] that PAC-learns k-parities with sample complexity O(klogn) can be extended to the mistake-bound model.