  A central question for active learning (AL) is: "what is the optimal
selection?" Defining optimality by classifier loss produces a new
characterisation of optimal AL behaviour, by treating expected loss reduction
as a statistical target for estimation. This target forms the basis of model
retraining improvement (MRI), a novel approach providing a statistical
estimation framework for AL. This framework is constructed to address the
central question of AL optimality, and to motivate the design of estimation
algorithms. MRI allows the exploration of optimal AL behaviour, and the
examination of AL heuristics, showing precisely how they make sub-optimal
selections. The abstract formulation of MRI is used to provide a new guarantee
for AL, that an unbiased MRI estimator should outperform random selection. This
MRI framework reveals intricate estimation issues that in turn motivate the
construction of new statistical AL algorithms. One new algorithm in particular
performs strongly in a large-scale experimental study, compared to standard AL
methods. This competitive performance suggests that practical efforts to
minimise estimation bias may be important for AL applications.
