Learning with queries corrupted by classification noise

Kearns introduced the `statistical query' (SQ) model as a general method for producing learning algorithms which are robust against classification noise. We extend this approach in several ways, in order to tackle algorithms that use `membership queries', focusing on the more stringent model of `persistent noise'. The main ingredients in the general analysis are: 1. Smallness of dimension of both the targets' class and the queries' class. 2. Independence of the noise variables. Persistence restricts independence, forcing repeated invocation of the same point x to give the same label. We apply the general analysis and ad-hoc considerations to get noise- robust version of Jackson's Harmonic Sieve, which learns DNF under the uniform distribution. This corrects an error in his earlier analysis of noise tolerant DNF learning.