  Predicated on the increasing abundance of electronic health records, we
investi- gate the problem of inferring individualized treatment effects using
observational data. Stemming from the potential outcomes model, we propose a
novel multi- task learning framework in which factual and counterfactual
outcomes are mod- eled as the outputs of a function in a vector-valued
reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian
method for learning the treatment effects using a multi-task Gaussian process
(GP) with a linear coregion- alization kernel as a prior over the vvRKHS. The
Bayesian approach allows us to compute individualized measures of confidence in
our estimates via pointwise credible intervals, which are crucial for realizing
the full potential of precision medicine. The impact of selection bias is
alleviated via a risk-based empirical Bayes method for adapting the multi-task
GP prior, which jointly minimizes the empirical error in factual outcomes and
the uncertainty in (unobserved) counter- factual outcomes. We conduct
experiments on observational datasets for an inter- ventional social program
applied to premature infants, and a left ventricular assist device applied to
cardiac patients wait-listed for a heart transplant. In both experi- ments, we
show that our method significantly outperforms the state-of-the-art.
