PAC Analogues of Perceptron and Winnow via Boosting the Margin

摘要

We describe a novel family of PAC model algorithms for learning linear threshold functions. The new algorithms work by boosting a simple weak learner and exhibit complexity bounds remarkably similar to those of known online algorithms such as Perceptron and Winnow, thus suggesting that these well-studied online algorithms in some sense correspond to instances of boosting. We show that the new algorithms can be viewed as natural PAC analogues of the online p-norm algorithms which have recently been studied by Grove, Littlestone, and Schuurmans and Gentile and Littlestone . As special cases of the algorithm, by taking p = 2 and p =∞ we obtain natural boosting-based PAC analogues of Perceptron and Winnow respectively. The p = ∞ case of our algorithm can also be viewed as a generalization (with an improved sample complexity bound) of Jackson and Craven's PAC-model boosting-based algorithm for learning "sparse perceptrons". The analysis of the generalization error of the new algorithms relies on techniques from the theory of large margin classification.