mlsanityData to 7 Oct 2026

Explanations for Monotonic Classifiers

arXiv 2106.00154 ↗First posted 1 Jun 2021cs.LG stat.MLcited by 39

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Abstract (arXiv)

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction. Despite comprehensive efforts on learning monotonic classifiers, dedicated approaches for explaining monotonic classifiers are scarce and classifier-specific. This paper describes novel algorithms for the computation of one formal explanation of a (black-box) monotonic classifier. These novel algorithms are polynomial in the run time complexity of the classifier and the number of features. Furthermore, the paper presents a practically efficient model-agnostic algorithm for enumerating formal explanations.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 22 of its 57 references that are in the map. First posted on arXiv 1 Jun 2021.

Builds on

22 of 57 references.

References · 22

  1. 2017A Unified Approach to Interpreting Model Predictionscited by 6,488
  2. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,040
  3. 2017Explanation in Artificial Intelligence: Insights from the Social Sciencescited by 1,201
  4. 2018Abduction-Based Explanations for Machine Learning Modelscited by 159
  5. 2018A Symbolic Approach to Explaining Bayesian Network Classifierscited by 130
  6. 2020On the Tractability of SHAP Explanationscited by 92
  7. 2017Deep Lattice Networks and Partial Monotonic Functionscited by 62
  8. 2021On Explaining Random Forests with SATcited by 57
  9. 2020Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delaycited by 56
  10. 2020Certified Monotonic Neural Networkscited by 51
  11. 2020On Explaining Decision Treescited by 49
  12. 2021On the Computational Intelligibility of Boolean Classifierscited by 40
10 more
  1. 2021SAT-Based Rigorous Explanations for Decision Listscited by 40
  2. 2015Monotonic Calibrated Interpolated Look-Up Tablescited by 35
  3. 2020On Tractable Representations of Binary Neural Networkscited by 34
  4. 2020Counterexample-Guided Learning of Monotonic Neural Networkscited by 34
  5. 2018Monotonic classification: an overview on algorithms, performance measures and data setscited by 18
  6. 2020Deontological Ethics By Monotonicity Shape Constraintscited by 16
  7. 2020On Symbolically Encoding the Behavior of Random Forestscited by 15
  8. 2020On Relating 'Why?' and 'Why Not?' Explanationscited by 15
  9. 2018Prediction Rule Reshapingcited by 3
  10. 2021Sufficient reasons for classifier decisions in the presence of constraintscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 9; 2023: 8; 2024: 3; 2025: 10; 2026: 7.

39 papers.

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  1. 2022Logic-Based Explainability in Machine Learningcited by 47
  2. 2022On Tackling Explanation Redundancy in Decision Treescited by 44
  3. 2021On Efficiently Explaining Graph-Based Classifierscited by 37
  4. 2021Defining and Quantifying the Emergence of Sparse Concepts in DNNscited by 36
  5. 2022On Computing Probabilistic Explanations for Decision Treescited by 35
  6. 2023The Inadequacy of Shapley Values for Explainabilitycited by 30
  7. 2022Eliminating The Impossible, Whatever Remains Must Be Truecited by 23
  8. 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
  9. 2022Feature Necessity & Relevancy in ML Classifier Explanationscited by 22
  10. 2022On Computing Probabilistic Abductive Explanationscited by 18
  11. 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanationscited by 13
  12. 2023Disproving XAI Myths with Formal Methods -- Initial Resultscited by 12
27 more
  1. 2024Model Reconstruction Using Counterfactual Explanations: A Perspective From Polytope Theorycited by 12
  2. 2023On Formal Feature Attribution and Its Approximationcited by 11
  3. 2024Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretationcited by 11
  4. 2025Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasonscited by 11
  5. 2023Axiomatic Aggregations of Abductive Explanationscited by 10
  6. 2025Explaining k-Nearest Neighbors: Abductive and Counterfactual Explanationscited by 10
  7. 2026Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guaranteescited by 10
  8. 2023Anytime Approximate Formal Feature Attributioncited by 9
  9. 2022Cardinality-Minimal Explanations for Monotonic Neural Networkscited by 8
  10. 2023A New Class of Explanations for Classifiers with Non-Binary Featurescited by 8
  11. 2022On Computing Relevant Features for Explaining NBCscited by 5
  12. 2023On the Complexity of Enumerating Prime Implicants from Decision-DNNF Circuitscited by 5
  13. 2025Sufficient, Necessary and Complete Causal Explanations in Image Classificationcited by 4
  14. 2025Faster Verified Explanations for Neural Networkscited by 4
  15. 2026FAME: Formal Abstract Minimal Explanation for Neural Networkscited by 3
  16. 2023Finding Minimum-Cost Explanations for Predictions made by Tree Ensemblescited by 1
  17. 2025Uncovering Bugs in Formal Explainers: A Case Study with PyXAIcited by 1
  18. 2025Sufficient Explanations in Databases and their Connections to Database Repairscited by 1
  19. 2026Axiomatic Foundations of Counterfactual Explanationscited by 1
  20. 2026Provably Explaining Neural Additive Modelscited by 1
  21. 2026Unifying Formal Explanations: A Complexity-Theoretic Perspectivecited by 1
  22. 2022Some recent advances in reasoning based on analogical proportionscited by 0
  23. 2025Ranking Counterfactual Explanationscited by 0
  24. 2025Interpretable DNFscited by 0
  25. 2025Efficient & Correct Predictive Equivalence for Decision Treescited by 0
  26. 2026Rigorous Explanations for Tree Ensemblescited by 0
  27. 2026Towards Rigorous Explainability by Feature Attributioncited by 0