In this paper, we study bootstrapping algorithms for learning from unlabeled data. The general idea in bootstrapping is to use some initial labeled data to build a (possibly partial) predictive labeling procedure; then use the labeling procedure to label more data; then use the newly labeled data to build a new predictive procedure and so on. This process can be iterated until a fixed point is reached or some other stopping criterion is met. Here we give P AC style bounds on generalization error which can be used to formally justify certain boostrapping algorithms. One well-known form of bootstrapping is the EM algorithm (Dempster, Laird and Rubin, 1977).

The rule-based bootstrapping introduced by Y arowsky, and its co-training 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 P ACstyle 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, i.e., where instances are to be assigned one of