  This paper analyses the fundamental ingredients behind surrogate explanations
to provide a better understanding of their inner workings. We start our
exposition by considering global surrogates, describing the trade-off between
complexity of the surrogate and fidelity to the black-box being modelled. We
show that transitioning from global to local - reducing coverage - allows for
more favourable conditions on the Pareto frontier of fidelity-complexity of a
surrogate. We discuss the interplay between complexity, fidelity and coverage,
and consider how different user needs can lead to problem formulations where
these are either constraints or penalties. We also present experiments that
demonstrate how the local surrogate interpretability procedure can be made
interactive and lead to better explanations.
