mlsanityData to 7 Oct 2026

Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice

arXiv 2103.14651 ↗First posted 27 Mar 2021cs.LG cs.AIcited by 45

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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.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). Builds on 37 of its 105 references that are in the map. First posted on arXiv 27 Mar 2021.

Builds on

37 of 105 references.

References · 37

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  3. 2017Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)cited by 1,309
  4. 2017Explanation in Artificial Intelligence: Insights from the Social Sciencescited by 1,201
  5. 2017Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPRcited by 1,086
  6. 2020Concept Bottleneck Modelscited by 1,022
  7. 2018Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representationscited by 929
  8. 2016The Mythos of Model Interpretabilitycited by 716
  9. 2019Explaining Machine Learning Classifiers through Diverse Counterfactual Explanationscited by 612
  10. 2021Interpretable Machine Learning: Fundamental Principles and 10 Grand Challengescited by 364
  11. 2019The many Shapley values for model explanationcited by 341
  12. 2018Actionable Recourse in Linear Classificationcited by 327
25 more
  1. 2019Interpretable machine learning: definitions, methods, and applicationscited by 303
  2. 2018Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negativescited by 261
  3. 2020Algorithmic Recourse: from Counterfactual Explanations to Interventionscited by 250
  4. 2019Explainable Machine Learning in Deploymentcited by 210
  5. 2019The What-If Tool: Interactive Probing of Machine Learning Modelscited by 207
  6. 2019Explaining individual predictions when features are dependent: More accurate approximations to Shapley valuescited by 205
  7. 2020Problems with Shapley-value-based explanations as feature importance measurescited by 198
  8. 2018Abduction-Based Explanations for Machine Learning Modelscited by 159
  9. 2015Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction modelcited by 140
  10. 2020Algorithmic recourse under imperfect causal knowledge: a probabilistic approachcited by 139
  11. 2020A survey of algorithmic recourse: definitions, formulations, solutions, and prospectscited by 118
  12. 2019The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasonscited by 115
  13. 2019"How do I fool you?": Manipulating User Trust via Misleading Black Box Explanationscited by 111
  14. 2020Causal Shapley Values: Exploiting Causal Knowledge to Explain Individual Predictions of Complex Modelscited by 107
  15. 2020On The Reasons Behind Decisionscited by 99
  16. 2013Probabilities of Causation: Bounds and Identificationcited by 89
  17. 2020Towards Unifying Feature Attribution and Counterfactual Explanations: Different Means to the Same Endcited by 66
  18. 2019Approximate Causal Abstractioncited by 62
  19. 2021Explaining Black-Box Algorithms Using Probabilistic Contrastive Counterfactualscited by 55
  20. 2021Causal Sufficiency and Actual Causationcited by 29
  21. 2019Counterfactual Explanation Algorithms for Behavioral and Textual Datacited by 26
  22. 2020Explaining Data-Driven Decisions made by AI Systems: The Counterfactual Approachcited by 26
  23. 2018Interpreting Neural Network Judgments via Minimal, Stable, and Symbolic Correctionscited by 19
  24. 2019Learning Representations by Humans, for Humanscited by 18
  25. 2020Causal Feature Learning for Utility-Maximizing Agentscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 8; 2023: 10; 2024: 13; 2025: 5; 2026: 5.

45 papers.

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  1. 2022Impossibility Theorems for Feature Attributioncited by 78
  2. 2021Desiderata for Representation Learning: A Causal Perspectivecited by 76
  3. 2023Explaining Predictive Uncertainty with Information Theoretic Shapley Valuescited by 36
  4. 2022Causal Explanations and XAIcited by 30
  5. 2023The Inadequacy of Shapley Values for Explainabilitycited by 30
  6. 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
  7. 2023Towards Trustworthy Explanation: On Causal Rationalizationcited by 19
  8. 2021Rational Shapley Valuescited by 18
  9. 2022Necessity and Sufficiency for Explaining Text Classifiers: A Case Study in Hate Speech Detectioncited by 18
  10. 2023The role of causality in explainable artificial intelligencecited by 17
  11. 2024Reconsidering Faithfulness in Regular, Self-Explainable and Domain Invariant GNNscited by 14
  12. 2022On the Probability of Necessity and Sufficiency of Explaining Graph Neural Networks: A Lower Bound Optimization Approachcited by 11
33 more
  1. 2025Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasonscited by 11
  2. 2023Axiomatic Aggregations of Abductive Explanationscited by 10
  3. 2022XInsight: eXplainable Data Analysis Through The Lens of Causalitycited by 9
  4. 2023The Utility of "Even if..." Semifactual Explanation to Optimise Positive Outcomescited by 8
  5. 2024Probabilities of Causation for Continuous and Vector Variablescited by 8
  6. 2024Feature Attribution with Necessity and Sufficiency via Dual-stage Perturbation Test for Causal Explanationcited by 6
  7. 2024Beyond Model Interpretability: Socio-Structural Explanations in Machine Learningcited by 6
  8. 2023SUNY: A Visual Interpretation Framework for Convolutional Neural Networks from a Necessary and Sufficient Perspectivecited by 5
  9. 2022Explaining Image Classifiers Using Contrastive Counterfactuals in Generative Latent Spacescited by 4
  10. 2023A Refutation of Shapley Values for Explainabilitycited by 4
  11. 2022Local Interpretable Model Agnostic Shap Explanations for machine learning modelscited by 3
  12. 2023Concept-Based Explanations to Test for False Causal Relationships Learned by Abusive Language Classifierscited by 3
  13. 2024Unifying Invariance and Spuriousity for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 3
  14. 2024Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairnesscited by 3
  15. 2024Sufficient and Necessary Explanations (and What Lies in Between)cited by 3
  16. 2021When Stability meets Sufficiency: Informative Explanations that do not Overwhelmcited by 2
  17. 2023Fixing confirmation bias in feature attribution methods via semantic matchcited by 2
  18. 2024SIDEs: Separating Idealization from Deceptive Explanations in xAIcited by 2
  19. 2024Challenges and Opportunities in Text Generation Explainabilitycited by 2
  20. 2024Are Objective Explanatory Evaluation metrics Trustworthy? An Adversarial Analysiscited by 2
  21. 2024Unifying Invariant and Variant Features for Graph Out-of-Distribution via Probability of Necessity and Sufficiencycited by 2
  22. 2024Monetizing Currency Pair Sentiments through LLM Explainabilitycited by 2
  23. 2025Attribution Explanations for Deep Neural Networks: A Theoretical Perspectivecited by 2
  24. 2021Model Explanations via the Axiomatic Causal Lenscited by 1
  25. 2025Learning Probabilities of Causation with Mask-Augmented Datacited by 1
  26. 2026A unified framework for evaluating the robustness of machine-learning interpretability for prospect riskingcited by 1
  27. 2022Effective Explanations for Entity Resolution Modelscited by 0
  28. 2025Fixed Point Explainabilitycited by 0
  29. 2025Unifying Post-hoc Explanations of Knowledge Graph Completionscited by 0
  30. 2026Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variablescited by 0
  31. 2026Explainable Control Framework (XCF) based on Fuzzy Model-Agnostic Explanation and LLM Agent-Supported Interfacecited by 0
  32. 2026Regional Explanations via Causal Sufficiency and Necessitycited by 0
  33. 2026Where MLLMs Fail and Why: Causal Task Decomposition for Capability Failure Diagnosiscited by 0