  Counterfactual explanations have emerged as an important tool to understand,
debug, and audit complex machine learning models. To offer global
counterfactual explainability, state-of-the-art methods construct summaries of
local explanations, offering a trade-off among conciseness, counterfactual
effectiveness, and counterfactual cost or burden imposed on instances. In this
work, we provide a concise formulation of the problem of identifying global
counterfactuals and establish principled criteria for comparing solutions,
drawing inspiration from Pareto dominance. We introduce innovative algorithms
designed to address the challenge of finding global counterfactuals for either
the entire input space or specific partitions, employing clustering and
decision trees as key components. Additionally, we conduct a comprehensive
experimental evaluation, considering various instances of the problem and
comparing our proposed algorithms with state-of-the-art methods. The results
highlight the consistent capability of our algorithms to generate meaningful
and interpretable global counterfactual explanations.
