# Regional Explanations via Causal Sufficiency and Necessity

arXiv: https://arxiv.org/abs/2609.18049 · HTML: https://mlsanity.com/paper/2609.18049/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 42 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 19 of 19)

- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability](https://mlsanity.com/paper/2301.04709/) (2023)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Learning and Evaluating Graph Neural Network Explanations based on Counterfactual and Factual Reasoning](https://mlsanity.com/paper/2202.08816/) (2022)
- [Scalable Bayesian Rule Lists](https://mlsanity.com/paper/1602.08610/) (2016)
- [Falling Rule Lists](https://mlsanity.com/paper/1411.5899/) (2014)
- [Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactuals](https://mlsanity.com/paper/2103.11972/) (2021)
- [Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice](https://mlsanity.com/paper/2103.14651/) (2021)
- [Scalable Rule-Based Representation Learning for Interpretable Classification](https://mlsanity.com/paper/2109.15103/) (2021)
- [Learning Accurate and Interpretable Decision Rule Sets from Neural Networks](https://mlsanity.com/paper/2103.02826/) (2021)
- [Disentangled Explanations of Neural Network Predictions by Finding Relevant Subspaces](https://mlsanity.com/paper/2212.14855/) (2022)
- [Necessity and Sufficiency for Explaining Text Classifiers: A Case Study in Hate Speech Detection](https://mlsanity.com/paper/2205.03302/) (2022)
- [Interpretable multiclass classification by MDL-based rule lists](https://mlsanity.com/paper/1905.00328/) (2019)
- [On the Probability of Necessity and Sufficiency of Explaining Graph Neural Networks: A Lower Bound Optimization Approach](https://mlsanity.com/paper/2212.07056/) (2022)
- [Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation](https://mlsanity.com/paper/2402.08845/) (2024)
- [PAGE: Prototype-Based Model-Level Explanations for Graph Neural Networks](https://mlsanity.com/paper/2210.17159/) (2022)
- [Scalable Rule Lists Learning with Sampling](https://mlsanity.com/paper/2406.12803/) (2024)

## Abstract (arXiv)

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.