  Proxy causal learning (PCL) is a method for estimating the causal effect of
treatments on outcomes in the presence of unobserved confounding, using proxies
(structured side information) for the confounder. This is achieved via
two-stage regression: in the first stage, we model relations among the
treatment and proxies; in the second stage, we use this model to learn the
effect of treatment on the outcome, given the context provided by the proxies.
PCL guarantees recovery of the true causal effect, subject to identifiability
conditions. We propose a novel method for PCL, the deep feature proxy variable
method (DFPV), to address the case where the proxies, treatments, and outcomes
are high-dimensional and have nonlinear complex relationships, as represented
by deep neural network features. We show that DFPV outperforms recent
state-of-the-art PCL methods on challenging synthetic benchmarks, including
settings involving high dimensional image data. Furthermore, we show that PCL
can be applied to off-policy evaluation for the confounded bandit problem, in
which DFPV also exhibits competitive performance.
