  Counterfactual explanations provide a potentially significant solution to the
Explainable AI (XAI) problem, but good, native counterfactuals have been shown
to rarely occur in most datasets. Hence, the most popular methods generate
synthetic counterfactuals using blind perturbation. However, such methods have
several shortcomings: the resulting counterfactuals (i) may not be valid
data-points (they often use features that do not naturally occur), (ii) may
lack the sparsity of good counterfactuals (if they modify too many features),
and (iii) may lack diversity (if the generated counterfactuals are minimal
variants of one another). We describe a method designed to overcome these
problems, one that adapts native counterfactuals in the original dataset, to
generate sparse, diverse synthetic counterfactuals from naturally occurring
features. A series of experiments are reported that systematically explore
parametric variations of this novel method on common datasets to establish the
conditions for optimal performance.
