  In this paper, we address the challenge of performing counterfactual
inference with observational data via Bayesian nonparametric regression
adjustment, with a focus on high-dimensional settings featuring multiple
actions and multiple correlated outcomes. We present a general class of
counterfactual multi-task deep kernels models that estimate causal effects and
learn policies proficiently thanks to their sample efficiency gains, while
scaling well with high dimensions. In the first part of the work, we rely on
Structural Causal Models (SCM) to formally introduce the setup and the problem
of identifying counterfactual quantities under observed confounding. We then
discuss the benefits of tackling the task of causal effects estimation via
stacked coregionalized Gaussian Processes and Deep Kernels. Finally, we
demonstrate the use of the proposed methods on simulated experiments that span
individual causal effects estimation, off-policy evaluation and optimization.
