  Estimating heterogeneous treatment effects is an important problem across
many domains. In order to accurately estimate such treatment effects, one
typically relies on data from observational studies or randomized experiments.
Currently, most existing works rely exclusively on observational data, which is
often confounded and, hence, yields biased estimates. While observational data
is confounded, randomized data is unconfounded, but its sample size is usually
too small to learn heterogeneous treatment effects. In this paper, we propose
to estimate heterogeneous treatment effects by combining large amounts of
observational data and small amounts of randomized data via representation
learning. In particular, we introduce a two-step framework: first, we use
observational data to learn a shared structure (in form of a representation);
and then, we use randomized data to learn the data-specific structures. We
analyze the finite sample properties of our framework and compare them to
several natural baselines. As such, we derive conditions for when combining
observational and randomized data is beneficial, and for when it is not. Based
on this, we introduce a sample-efficient algorithm, called CorNet. We use
extensive simulation studies to verify the theoretical properties of CorNet and
multiple real-world datasets to demonstrate our method's superiority compared
to existing methods.
