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The rule-based bootstrapping introduced by Yarowsky, and its cotraining variant by Blum and Mitchell, have met with considerable empirical success. Earlier work on the theory of co-training has been only loosely related to empirically useful co-training algorithms. Here we give a new PAC-style bound on generalization error which justifies both the use of confidences—partial rules and partial labeling of the unlabeled data—and the use of an agreement-based objective function as suggested by Collins and Singer. Our bounds apply to the multiclass case, ie, where instances are to be assigned one of labels for