  Active learning can reduce the number of samples needed to perform a
hypothesis test and to estimate the parameters of a model. In this paper, we
revisit the work of Chernoff that described an asymptotically optimal algorithm
for performing a hypothesis test. We obtain a novel sample complexity bound for
Chernoff's algorithm, with a non-asymptotic term that characterizes its
performance at a fixed confidence level. We also develop an extension of
Chernoff sampling that can be used to estimate the parameters of a wide variety
of models and we obtain a non-asymptotic bound on the estimation error. We
apply our extension of Chernoff sampling to actively learn neural network
models and to estimate parameters in real-data linear and non-linear regression
problems, where our approach performs favorably to state-of-the-art methods.
