  In this paper we propose and study a generalization of the standard
active-learning model where a more general type of query, class conditional
query, is 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 two 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.
