  Consider the problem of improving the estimation of conditional average
treatment effects (CATE) for a target domain of interest by leveraging related
information from a source domain with a different feature space. This
heterogeneous transfer learning problem for CATE estimation is ubiquitous in
areas such as healthcare where we may wish to evaluate the effectiveness of a
treatment for a new patient population for which different clinical covariates
and limited data are available. In this paper, we address this problem by
introducing several building blocks that use representation learning to handle
the heterogeneous feature spaces and a flexible multi-task architecture with
shared and private layers to transfer information between potential outcome
functions across domains. Then, we show how these building blocks can be used
to recover transfer learning equivalents of the standard CATE learners. On a
new semi-synthetic data simulation benchmark for heterogeneous transfer
learning we not only demonstrate performance improvements of our heterogeneous
transfer causal effect learners across datasets, but also provide insights into
the differences between these learners from a transfer perspective.
