  The instrumental variable (IV) approach is a widely used way to estimate the
causal effects of a treatment on an outcome of interest from observational data
with latent confounders. A standard IV is expected to be related to the
treatment variable and independent of all other variables in the system.
However, it is challenging to search for a standard IV from data directly due
to the strict conditions. The conditional IV (CIV) method has been proposed to
allow a variable to be an instrument conditioning on a set of variables,
allowing a wider choice of possible IVs and enabling broader practical
applications of the IV approach. Nevertheless, there is not a data-driven
method to discover a CIV and its conditioning set directly from data. To fill
this gap, in this paper, we propose to learn the representations of the
information of a CIV and its conditioning set from data with latent confounders
for average causal effect estimation. By taking advantage of deep generative
models, we develop a novel data-driven approach for simultaneously learning the
representation of a CIV from measured variables and generating the
representation of its conditioning set given measured variables. Extensive
experiments on synthetic and real-world datasets show that our method
outperforms the existing IV methods.
