  Feature attribution for kernel methods is often heuristic and not
individualised for each prediction. To address this, we turn to the concept of
Shapley values~(SV), a coalition game theoretical framework that has previously
been applied to different machine learning model interpretation tasks, such as
linear models, tree ensembles and deep networks. By analysing SVs from a
functional perspective, we propose \textsc{RKHS-SHAP}, an attribution method
for kernel machines that can efficiently compute both \emph{Interventional} and
\emph{Observational Shapley values} using kernel mean embeddings of
distributions. We show theoretically that our method is robust with respect to
local perturbations - a key yet often overlooked desideratum for consistent
model interpretation. Further, we propose \emph{Shapley regulariser},
applicable to a general empirical risk minimisation framework, allowing
learning while controlling the level of specific feature's contributions to the
model. We demonstrate that the Shapley regulariser enables learning which is
robust to covariate shift of a given feature and fair learning which controls
the SVs of sensitive features.
