  Estimating conditional average treatment effects (CATE) is challenging,
especially when treatment information is missing. Although this is a widespread
problem in practice, CATE estimation with missing treatments has received
little attention. In this paper, we analyze CATE estimation in the setting with
missing treatments where unique challenges arise in the form of covariate
shifts. We identify two covariate shifts in our setting: (i) a covariate shift
between the treated and control population; and (ii) a covariate shift between
the observed and missing treatment population. We first theoretically show the
effect of these covariate shifts by deriving a generalization bound for
estimating CATE in our setting with missing treatments. Then, motivated by our
bound, we develop the missing treatment representation network (MTRNet), a
novel CATE estimation algorithm that learns a balanced representation of
covariates using domain adaptation. By using balanced representations, MTRNet
provides more reliable CATE estimates in the covariate domains where the data
are not fully observed. In various experiments with semi-synthetic and
real-world data, we show that our algorithm improves over the state-of-the-art
by a substantial margin.
