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There is an emerging interest in generating robust counterfactualexplanations that would remain valid if the model is updated or changed evenslightly. Towards finding robust counterfactuals, existing literature oftenassumes that the original model $m$ and the new model $M$ are bounded in theparameter space, i.e., $\|\text{Params}(M){-}\text{Params}(m)\|{<}\Delta$.However, models can often change significantly in the parameter space withlittle to no change in their predictions or accuracy on the given dataset. Inthis work, we introduce a mathematical abstraction termed\emph{naturally-occurring} model change, which allows for arbitrary changes inthe parameter space such that the change in predictions on points that lie onthe data manifold is limited. Next, we propose a measure -- that we call\emph{Stability} -- to quantify the robustness of counterfactuals to potentialmodel changes for differentiable models, e.g., neural networks. Our maincontribution is to show that counterfactuals with sufficiently high value of\emph{Stability} as defined by our measure will remain valid after potential``naturally-occurring'' model changes with high probability (leveragingconcentration bounds for Lipschitz function of independent Gaussians). Sinceour quantification depends on the local Lipschitz constant around a data pointwhich is not always available, we also examine practical relaxations of ourproposed measure and demonstrate experimentally how they can be incorporated tofind robust counterfactuals for neural networks that are close, realistic, andremain valid after potential model changes. This work also has interestingconnections with model multiplicity, also known as, the Rashomon effect.

Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees