  Expanding on MacKay (1992), we argue that conventional model-based methods
for active learning - like BALD - have a fundamental shortfall: they fail to
directly account for the test-time distribution of the input variables. This
can lead to pathologies in the acquisition strategy, as what is maximally
informative for model parameters may not be maximally informative for
prediction: for example, when the data in the pool set is more dispersed than
that of the final prediction task, or when the distribution of pool and test
samples differs. To correct this, we revisit an acquisition strategy that is
based on maximizing the expected information gained about possible future
predictions, referring to this as the Expected Predictive Information Gain
(EPIG). As EPIG does not scale well for batch acquisition, we further examine
an alternative strategy, a hybrid between BALD and EPIG, which we call the
Joint Expected Predictive Information Gain (JEPIG). We consider using both for
active learning with Bayesian neural networks on a variety of datasets,
examining the behavior under distribution shift in the pool set.
