  The choice of making an intervention depends on its potential benefit or harm
in comparison to alternatives. Estimating the likely outcome of alternatives
from observational data is a challenging problem as all outcomes are never
observed, and selection bias precludes the direct comparison of differently
intervened groups. Despite their empirical success, we show that algorithms
that learn domain-invariant representations of inputs (on which to make
predictions) are often inappropriate, and develop generalization bounds that
demonstrate the dependence on domain overlap and highlight the need for
invertible latent maps. Based on these results, we develop a deep kernel
regression algorithm and posterior regularization framework that substantially
outperforms the state-of-the-art on a variety of benchmarks data sets.
