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# Active Boosted Learning (ActBoost)

*Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics*, PMLR 15:743-751, 2011.

#### Abstract

Active learning deals with the problem of selecting a small subset of examples to label, from a pool of unlabeled data, for training a good classifier. We develop an active learning algorithm algorithm in the boosting framework. In contrast to much of the recent efforts, which has focused on selecting the most ambiguous unlabeled example to label based on the current learned classifier, our algorithm selects examples to maximally reduce the volume of the version space of feasible boosted classifiers. We show that under suitable sparsity assumptions, this strategy achieves the generalization error performance of a boosted classifier trained on the entire data set while only selecting logarithmically many unlabeled samples to label. We also establish a partial negative result, in that with out imposing structural assumptions it is difficult to guarantee generalization error performance. We explicitly characterize our convergence rate in terms of the sign pattern differences produced by the weak learners on the unlabeled data. We also present a convex relaxation to account for the non-convex sparse structure and show that the computational complexity of the resulting algorithm scales polynomially in the number of weak learners. We test ActBoost on several datasets to illustrate its performance and demonstrate its robustness to initialization.