  With the increasing impact of algorithmic decision-making on human lives, the
interpretability of models has become a critical issue in machine learning.
Counterfactual explanation is an important method in the field of interpretable
machine learning, which can not only help users understand why machine learning
models make specific decisions, but also help users understand how to change
these decisions. Naturally, it is an important task to study the robustness of
counterfactual explanation generation algorithms to model changes. Previous
literature has proposed the concept of Naturally-Occurring Model Change, which
has given us a deeper understanding of robustness to model change. In this
paper, we first further generalize the concept of Naturally-Occurring Model
Change, proposing a more general concept of model parameter changes,
Generally-Occurring Model Change, which has a wider range of applicability. We
also prove the corresponding probabilistic guarantees. In addition, we consider
a more specific problem, data set perturbation, and give relevant theoretical
results by combining optimization theory.
