  We consider the problem of noisy Bayesian active learning, where we are given
a finite set of functions $\mathcal{H}$, a sample space $\mathcal{X}$, and a
label set $\mathcal{L}$. One of the functions in $\mathcal{H}$ assigns labels
to samples in $\mathcal{X}$. The goal is to identify the function that
generates the labels even though the result of a label query on a sample is
corrupted by independent noise. More precisely, the objective is to declare one
of the functions in $\mathcal{H}$ as the true label generating function with
high confidence using as few label queries as possible, by selecting the
queries adaptively and in a strategic manner.
  Previous work in Bayesian active learning considers Generalized Binary
Search, and its variants for the noisy case, and analyzes the number of queries
required by these sampling strategies. In this paper, we show that these
schemes are, in general, suboptimal. Instead we propose and analyze an
alternative strategy for sample collection. Our sampling strategy is motivated
by a connection between Bayesian active learning and active hypothesis testing,
and is based on querying the label of a sample which maximizes the Extrinsic
Jensen-Shannon divergence at each step. We provide upper and lower bounds on
the performance of this sampling strategy, and show that these bounds are
better than previous bounds.
