  An active learner is given a hypothesis class, a large set of unlabeled
examples and the ability to interactively query labels to an oracle of a subset
of these examples; the goal of the learner is to learn a hypothesis in the
class that fits the data well by making as few label queries as possible.
  This work addresses active learning with labels obtained from strong and weak
labelers, where in addition to the standard active learning setting, we have an
extra weak labeler which may occasionally provide incorrect labels. An example
is learning to classify medical images where either expensive labels may be
obtained from a physician (oracle or strong labeler), or cheaper but
occasionally incorrect labels may be obtained from a medical resident (weak
labeler). Our goal is to learn a classifier with low error on data labeled by
the oracle, while using the weak labeler to reduce the number of label queries
made to this labeler. We provide an active learning algorithm for this setting,
establish its statistical consistency, and analyze its label complexity to
characterize when it can provide label savings over using the strong labeler
alone.
