Learning Parities in the Mistake-Bound model

We study the problem of learning parity functions that depend on at most k variables (kparities) attribute-efficiently in the mistake-bound model. We design a simple, deterministic, polynomial-time algorithm for learning k-parities with mistake bound O(n1− 1 k ). This is the first polynomial-time algorithm to learn ω(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 [1] for learning k-parities in the PAC model. We also show that the Õ(n) time algorithm from [1] that PAC-learns k-parities with sample complexity O(k log n) can be extended to the mistake-bound model.