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In this paper we propose and study a generalization of the standard active-learning model where a more general type of queries including class conditional queries and mistake queries are allowed. Such queries have been quite useful in applications, but have been lacking theoretical understanding. In this work, we characterize the power of such queries under several well-known noise models. We give nearly tight upper and lower bounds on the number of queries needed to learn both for the general agnostic setting and for the bounded noise model. We further show that our methods can be made adaptive to the (unknown) noise rate, with only negligible loss in query complexity.
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