Regional Explanations via Causal Sufficiency and Necessity

Model explainability is essential for understanding and trusting machine learning models. Existing explainable AI methods often explain predictions through feature importance, counterfactual explanations, or rules. However, a region-level characterization of when and only when a prediction behavior arises remains less explored. This paper proposes Causal Sufficient and Necessary Regional Explanations (SNRE), a framework that learns an input region $A$ and output region $B$ such that membership in $A$ is both sufficient and necessary for the model output to fall in $B$. Motivated by the classical Probability of Necessity and Sufficiency (PNS), we formulate a region-level PNS measure through stochastic interventions and derive a differentiable finite-sample estimator for optimization. SNRE parameterizes the input-output region pair with explicit and interpretable algebraic region families, together with a learnable feature mask, balancing expressiveness and interpretability. Experiments demonstrate that SNRE learns region pairs with strong sufficiency-necessity performance, robust explanation behavior, and practical utility for model analysis.