  Estimating personalized treatment effects from high-dimensional observational
data is essential in situations where experimental designs are infeasible,
unethical, or expensive. Existing approaches rely on fitting deep models on
outcomes observed for treated and control populations. However, when measuring
individual outcomes is costly, as is the case of a tumor biopsy, a
sample-efficient strategy for acquiring each result is required. Deep Bayesian
active learning provides a framework for efficient data acquisition by
selecting points with high uncertainty. However, existing methods bias training
data acquisition towards regions of non-overlapping support between the treated
and control populations. These are not sample-efficient because the treatment
effect is not identifiable in such regions. We introduce causal, Bayesian
acquisition functions grounded in information theory that bias data acquisition
towards regions with overlapping support to maximize sample efficiency for
learning personalized treatment effects. We demonstrate the performance of the
proposed acquisition strategies on synthetic and semi-synthetic datasets IHDP
and CMNIST and their extensions, which aim to simulate common dataset biases
and pathologies.
