  The benefit of locality is one of the major premises of LIME, one of the most
prominent methods to explain black-box machine learning models. This emphasis
relies on the postulate that the more locally we look at the vicinity of an
instance, the simpler the black-box model becomes, and the more accurately we
can mimic it with a linear surrogate. As logical as this seems, our findings
suggest that, with the current design of LIME, the surrogate model may
degenerate when the explanation is too local, namely, when the bandwidth
parameter $\sigma$ tends to zero. Based on this observation, the contribution
of this paper is twofold. Firstly, we study the impact of both the bandwidth
and the training vicinity on the fidelity and semantics of LIME explanations.
Secondly, and based on our findings, we propose \slime, an extension of LIME
that reconciles fidelity and locality.
