General Bounds on Statistical Query Learning and PAC Learning with Noise via Hypothesis Boosting

Abstract

We derive general bounds on the complexity of learning in the statistical query (SQ) model and in the PAC model with classification noise. We do so by considering the problem of boosting the accuracy of weak learning algorithms which fall within the SQ model. This new model was introduced by Kearns to provide a general framework for efficient PAC learning in the presence of classification noise. We first show a general scheme for boosting the accuracy of weak SQ learning algorithms, proving that weak SQ learning is equivalent to strong SQ learning. The boosting is efficient and is used to show our main result of the first general upper bounds on the complexity of strong SQ learning. Since all SQ algorithms can be simulated in the PAC model with classification noise, we also obtain general upper bounds on learning in the presence of classification noise for classes which can be learned in the SQ model.