Learning parities in the mistake-bound model

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 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 (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 ( k log n ) can be extended to the mistake-bound model.