Regional Explanations via Causal Sufficiency and Necessity

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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.