  Controlled interventions provide the most direct source of information for
learning causal effects. In particular, a dose-response curve can be learned by
varying the treatment level and observing the corresponding outcomes. However,
interventions can be expensive and time-consuming. Observational data, where
the treatment is not controlled by a known mechanism, is sometimes available.
Under some strong assumptions, observational data allows for the estimation of
dose-response curves. Estimating such curves nonparametrically is hard: sample
sizes for controlled interventions may be small, while in the observational
case a large number of measured confounders may need to be marginalized. In
this paper, we introduce a hierarchical Gaussian process prior that constructs
a distribution over the dose-response curve by learning from observational
data, and reshapes the distribution with a nonparametric affine transform
learned from controlled interventions. This function composition from different
sources is shown to speed-up learning, which we demonstrate with a thorough
sensitivity analysis and an application to modeling the effect of therapy on
cognitive skills of premature infants.
