  Modern instance-based model-agnostic explanation methods (LIME, SHAP, L2X)
are of great use in data-heavy industries for model diagnostics, and for
end-user explanations. These methods generally return either a weighting or
subset of input features as an explanation of the classification of an
instance. An alternative literature argues instead that counterfactual
instances provide a more useable characterisation of a black box classifier's
decisions. We present EMAP, a neural network based approach which returns as
Explanation the Minimal Adversarial Perturbation to an instance required to
cause the underlying black box model to missclassify. We show that this
approach combines the two paradigms, recovering the output of feature-weighting
methods in continuous feature spaces, whilst also indicating the direction in
which the nearest counterfactuals can be found. Our method also provides an
implicit confidence estimate in its own explanations, adding a clarity to model
diagnostics other methods lack. Additionally, EMAP improves upon the speed of
sampling-based methods such as LIME by an order of magnitude, allowing for
model explanations in time-critical applications, or at the dataset level,
where sampling-based methods are infeasible. We extend our approach to
categorical features using a partitioned Gumbel layer, and demonstrate its
efficacy on several standard datasets.
