  Instrumental variable (IV) regression is a standard strategy for learning
causal relationships between confounded treatment and outcome variables from
observational data by utilizing an instrumental variable, which affects the
outcome only through the treatment. In classical IV regression, learning
proceeds in two stages: stage 1 performs linear regression from the instrument
to the treatment; and stage 2 performs linear regression from the treatment to
the outcome, conditioned on the instrument. We propose a novel method, deep
feature instrumental variable regression (DFIV), to address the case where
relations between instruments, treatments, and outcomes may be nonlinear. In
this case, deep neural nets are trained to define informative nonlinear
features on the instruments and treatments. We propose an alternating training
regime for these features to ensure good end-to-end performance when composing
stages 1 and 2, thus obtaining highly flexible feature maps in a
computationally efficient manner. DFIV outperforms recent state-of-the-art
methods on challenging IV benchmarks, including settings involving high
dimensional image data. DFIV also exhibits competitive performance in
off-policy policy evaluation for reinforcement learning, which can be
understood as an IV regression task.
