  An active learner is given a class of models, a large set of unlabeled
examples, and the ability to interactively query labels of a subset of these
examples; the goal of the learner is to learn a model in the class that fits
the data well.
  Previous theoretical work has rigorously characterized label complexity of
active learning, but most of this work has focused on the PAC or the agnostic
PAC model. In this paper, we shift our attention to a more general setting --
maximum likelihood estimation. Provided certain conditions hold on the model
class, we provide a two-stage active learning algorithm for this problem. The
conditions we require are fairly general, and cover the widely popular class of
Generalized Linear Models, which in turn, include models for binary and
multi-class classification, regression, and conditional random fields.
  We provide an upper bound on the label requirement of our algorithm, and a
lower bound that matches it up to lower order terms. Our analysis shows that
unlike binary classification in the realizable case, just a single extra round
of interaction is sufficient to achieve near-optimal performance in maximum
likelihood estimation. On the empirical side, the recent work in
~\cite{Zhang12} and~\cite{Zhang14} (on active linear and logistic regression)
shows the promise of this approach.
