# Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice

arXiv: https://arxiv.org/abs/2103.14651 · HTML: https://mlsanity.com/paper/2103.14651/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 105 references that are in the map.
- First posted on arXiv 27 Mar 2021.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Explainable Machine Learning in Deployment](https://mlsanity.com/paper/1909.06342/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [The What-If Tool: Interactive Probing of Machine Learning Models](https://mlsanity.com/paper/1907.04135/) (2019)
- [Problems with Shapley-value-based explanations as feature importance measures](https://mlsanity.com/paper/2002.11097/) (2020)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model](https://mlsanity.com/paper/1511.01644/) (2015)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- ["How do I fool you?": Manipulating User Trust via Misleading Black Box Explanations](https://mlsanity.com/paper/1911.06473/) (2019)
- [Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Models](https://mlsanity.com/paper/2011.01625/) (2020)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Probabilities of Causation: Bounds and Identification](https://mlsanity.com/paper/1301.3898/) (2013)
- [Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same End](https://mlsanity.com/paper/2011.04917/) (2020)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)

## Built on by (most cited first, 30 of 45)

- [Impossibility Theorems for Feature Attribution](https://mlsanity.com/paper/2212.11870/) (2022)
- [Desiderata for Representation Learning: A Causal Perspective](https://mlsanity.com/paper/2109.03795/) (2021)
- [Explaining Predictive Uncertainty with Information Theoretic Shapley Values](https://mlsanity.com/paper/2306.05724/) (2023)
- [The Inadequacy of Shapley Values for Explainability](https://mlsanity.com/paper/2302.08160/) (2023)
- [Causal Explanations and XAI](https://mlsanity.com/paper/2201.13169/) (2022)
- [Local vs. Global Interpretability: A Computational Complexity Perspective](https://mlsanity.com/paper/2406.02981/) (2024)
- [Towards Trustworthy Explanation: On Causal Rationalization](https://mlsanity.com/paper/2306.14115/) (2023)
- [Rational Shapley Values](https://mlsanity.com/paper/2106.10191/) (2021)
- [Necessity and Sufficiency for Explaining Text Classifiers: A Case Study in Hate Speech Detection](https://mlsanity.com/paper/2205.03302/) (2022)
- [The role of causality in explainable artificial intelligence](https://mlsanity.com/paper/2309.09901/) (2023)
- [Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNs](https://mlsanity.com/paper/2406.15156/) (2024)
- [Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasons](https://mlsanity.com/paper/2502.03391/) (2025)
- [On the Probability of Necessity and Sufficiency of Explaining Graph Neural Networks: A Lower Bound Optimization Approach](https://mlsanity.com/paper/2212.07056/) (2022)
- [Axiomatic Aggregations of Abductive Explanations](https://mlsanity.com/paper/2310.03131/) (2023)
- [XInsight: eXplainable Data Analysis Through The Lens of Causality](https://mlsanity.com/paper/2207.12718/) (2022)
- [The Utility of "Even if..." Semifactual Explanation to Optimise Positive Outcomes](https://mlsanity.com/paper/2310.18937/) (2023)
- [Probabilities of Causation for Continuous and Vector Variables](https://mlsanity.com/paper/2405.20487/) (2024)
- [Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanation](https://mlsanity.com/paper/2402.08845/) (2024)
- [Beyond Model Interpretability: Socio-Structural Explanations in Machine Learning](https://mlsanity.com/paper/2409.03632/) (2024)
- [SUNY: A Visual Interpretation Framework for Convolutional Neural Networks from a Necessary and Sufficient Perspective](https://mlsanity.com/paper/2303.00244/) (2023)
- [Explaining Image Classifiers Using Contrastive Counterfactuals in Generative Latent Spaces](https://mlsanity.com/paper/2206.05257/) (2022)
- [A Refutation of Shapley Values for Explainability](https://mlsanity.com/paper/2309.03041/) (2023)
- [Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness](https://mlsanity.com/paper/2408.03425/) (2024)
- [Local Interpretable Model Agnostic Shap Explanations for machine learning models](https://mlsanity.com/paper/2210.04533/) (2022)
- [Concept-Based Explanations to Test for False Causal Relationships Learned by Abusive Language Classifiers](https://mlsanity.com/paper/2307.01900/) (2023)
- [Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiency](https://mlsanity.com/paper/2402.09165/) (2024)
- [Sufficient and Necessary Explanations (and What Lies in Between)](https://mlsanity.com/paper/2409.20427/) (2024)
- [When Stability meets Sufficiency: Informative Explanations that do not Overwhelm](https://mlsanity.com/paper/2109.06181/) (2021)
- [Fixing confirmation bias in feature attribution methods via semantic match](https://mlsanity.com/paper/2307.00897/) (2023)
- [SIDEs: Separating Idealization from Deceptive Explanations in xAI](https://mlsanity.com/paper/2404.16534/) (2024)

## Abstract (arXiv)

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks.