  We propose a new active learning algorithm for parametric linear regression
with random design. We provide finite sample convergence guarantees for general
distributions in the misspecified model. This is the first active learner for
this setting that provably can improve over passive learning. Unlike other
learning settings (such as classification), in regression the passive learning
rate of $O(1/\epsilon)$ cannot in general be improved upon. Nonetheless, the
so-called `constant' in the rate of convergence, which is characterized by a
distribution-dependent risk, can be improved in many cases. For a given
distribution, achieving the optimal risk requires prior knowledge of the
distribution. Following the stratification technique advocated in Monte-Carlo
function integration, our active learner approaches the optimal risk using
piecewise constant approximations.
