{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,5]],"date-time":"2026-08-05T01:13:26Z","timestamp":1785892406783,"version":"3.56.0"},"reference-count":98,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Artif. Intell."],"abstract":"<jats:p>Recent years witnessed a number of proposals for the use of the so-called interpretable models in specific application domains. These include high-risk, but also safety-critical domains. In contrast, other works reported some pitfalls of machine learning model interpretability, in part justified by the lack of a rigorous definition of what an interpretable model should represent. This study proposes to relate interpretability with the ability of a model to offer explanations of why a prediction is made given some point in feature space. Under this general goal of offering explanations to predictions, this study reveals additional limitations of interpretable models. Concretely, this study considers application domains where the purpose is to help human decision makers to understand why some prediction was made or why was not some other prediction made, and where irreducible (and so minimal) information is sought. In such domains, this study argues that answers to such why (or why not) questions can exhibit arbitrary redundancy, i.e., the answers can be simplified, as long as these answers are obtained by human inspection of the interpretable ML model representation.<\/jats:p>","DOI":"10.3389\/frai.2023.1128212","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T04:30:57Z","timestamp":1682310657000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["No silver bullet: interpretable ML models must be explained"],"prefix":"10.3389","volume":"6","author":[{"given":"Joao","family":"Marques-Silva","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexey","family":"Ignatiev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"B1","first-page":"19","article-title":"\u201cNon-monotonic explanation functions,\u201d","volume-title":"ECSQARU","author":"Amgoud","year":"2021"},{"key":"B2","first-page":"636","article-title":"\u201cAxiomatic foundations of explainability,\u201d","volume-title":"IJCAI","author":"Amgoud","year":"2022"},{"key":"B3","first-page":"11690","article-title":"\u201cFoundations of symbolic languages for model interpretability,\u201d","volume-title":"NeurIPS","author":"Arenas","year":"2021"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2207.12213","article-title":"On computing probabilistic explanations for decision trees","author":"Arenas","year":"2022","journal-title":"CoRR"},{"key":"B5","first-page":"79","article-title":"\u201cFair and adequate explanations,\u201d","author":"Asher","year":"2021","journal-title":"CD-MAKE"},{"key":"B6","first-page":"74","article-title":"\u201cOn the computational intelligibility of boolean classifiers,\u201d","author":"Audemard","year":"2021","journal-title":"KR"},{"key":"B7","first-page":"643","article-title":"\u201cOn preferred abductive explanations for decision trees and random forests,\u201d","volume-title":"IJCAI","author":"Audemard","year":""},{"key":"B8","first-page":"5461","article-title":"\u201cTrading complexity for sparsity in random forest explanations,\u201d","volume-title":"AAAI","author":"Audemard","year":""},{"key":"B9","first-page":"838","article-title":"\u201cOn tractable XAI queries based on compiled representations,\u201d","volume-title":"KR","author":"Audemard","year":"2020"},{"key":"B10","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1145\/3448250","article-title":"Deep learning for AI","volume":"64","author":"Bengio","year":"2021","journal-title":"Commun. ACM"},{"key":"B11","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1007\/s10994-017-5633-9","article-title":"Optimal classification trees","volume":"106","author":"Bertsimas","year":"2017","journal-title":"Mach. Learn"},{"key":"B12","doi-asserted-by":"crossref","DOI":"10.3233\/FAIA336","volume-title":"Handbook of Satisfiability","author":"Biere","year":"2021"},{"key":"B13","first-page":"623","article-title":"\u201cThe query complexity of certification,\u201d","volume-title":"STOC","author":"Blanc","year":""},{"key":"B14","first-page":"2075","article-title":"\u201cA query-optimal algorithm for finding counterfactuals,\u201d","volume-title":"ICML","author":"Blanc","year":""},{"key":"B15","article-title":"\u201cProvably efficient, succinct, and precise explanations,\u201d","volume-title":"NeurIPS","author":"Blanc","year":"2021"},{"key":"B16","first-page":"270","article-title":"\u201cA symbolic approach for counterfactual explanations,\u201d","volume-title":"SUM","author":"Boumazouza","year":"2020"},{"key":"B17","first-page":"120","article-title":"\u201cASTERYX: a model-agnostic sat-based approach for symbolic and score-based explanations,\u201d","volume-title":"CIKM","author":"Boumazouza","year":"2021"},{"key":"B18","first-page":"151","article-title":"\u201cRule induction with CN2: some recent improvements,\u201d","volume-title":"EWSL","author":"Clark","year":"1991"},{"key":"B19","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/BF00116835","article-title":"The CN2 induction algorithm","volume":"3","author":"Clark","year":"1989","journal-title":"Mach. Learn"},{"key":"B20","first-page":"151","article-title":"\u201cThe complexity of theorem-proving procedures,\u201d","volume-title":"STOC","author":"Cook","year":"1971"},{"key":"B21","first-page":"1","article-title":"\u201cOn the tractability of explaining decisions of classifiers,\u201d","volume-title":"CP","author":"Cooper","year":"2021"},{"key":"B22","first-page":"229","article-title":"\u201cThree modern roles for logic in AI,\u201d","volume-title":"PODS","author":"Darwiche","year":"2020"},{"key":"B23","first-page":"712","article-title":"\u201cOn the reasons behind decisions,\u201d","volume-title":"ECAI","author":"Darwiche","year":"2020"},{"key":"B24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10849-022-09377-8","article-title":"On the (complete) reasons behind decisions","volume":"2022","author":"Darwiche","year":"2022","journal-title":"J. Logic Lang. Inf"},{"key":"B25","doi-asserted-by":"publisher","first-page":"12756","DOI":"10.1613\/jair.1.12756","article-title":"On quantifying literals in boolean logic and its applications to explainable AI","volume":"2021","author":"Darwiche","year":"2021","journal-title":"J. Artif. Intell. Res"},{"key":"B26","unstructured":"FairML\n          Auditing Black-Box Predictive Models2016"},{"key":"B27","first-page":"432","article-title":"\u201cLooking inside the black-box: logic-based explanations for neural networks,\u201d","volume-title":"KR","author":"Ferreira","year":"2022"},{"key":"B28","author":"Flach","year":"2012","journal-title":"Machine Learning"},{"key":"B29","unstructured":"FriedlerS.\n            ScheideggerC.\n            VenkatasubramanianS.\n          33315263On Algorithmic Fairness, Discrimination and Disparate Impact2015"},{"key":"B30","doi-asserted-by":"publisher","DOI":"10.1016\/j.cmpb.2020.105400","article-title":"Decision tree-based diagnosis of coronary artery disease: CART model","author":"Ghiasi","year":"2020","journal-title":"Comput. Methods Programs Biomed"},{"key":"B31","author":"Goodfellow","year":"2016","journal-title":"Deep Learning. Adaptive Computation and Machine Learning"},{"key":"B32","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1145\/3422622","article-title":"Generative adversarial networks","volume":"63","author":"Goodfellow","year":"2020","journal-title":"Commun. ACM"},{"key":"B33","article-title":"\u201cExplaining and harnessing adversarial examples,\u201d","author":"Goodfellow","year":"2015","journal-title":"ICLR"},{"key":"B34","doi-asserted-by":"crossref","DOI":"10.1609\/aaai.v36i5.20507","article-title":"\u201cSufficient reasons for classifier decisions in the presence of domain constraints,\u201d","author":"Gorji","year":"2022","journal-title":"AAAI"},{"key":"B35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3236009","article-title":"A survey of methods for explaining black box models","volume":"93","author":"Guidotti","year":"2019","journal-title":"ACM Comput. Surv"},{"key":"B36","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1145\/3301275.3308446","article-title":"DARPA's explainable artificial intelligence (XAI) program","volume":"40","author":"Gunning","year":"2019","journal-title":"AI Mag"},{"key":"B37","first-page":"7265","article-title":"\u201cOptimal sparse decision trees,\u201d","author":"Hu","year":"2019","journal-title":"NeurIPS"},{"key":"B38","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2107.01654","article-title":"Efficient explanations for knowledge compilation languages","author":"Huang","year":"","journal-title":"CoRR"},{"key":"B39","doi-asserted-by":"crossref","first-page":"5719","DOI":"10.1609\/aaai.v36i5.20514","article-title":"\u201cTractable explanations for d-DNNF classifiers,\u201d","author":"Huang","year":"2022","journal-title":"AAAI"},{"key":"B40","first-page":"356","article-title":"\u201cOn efficiently explaining graph-based classifiers,\u201d","author":"Huang","year":"","journal-title":"KR"},{"key":"B41","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2202.07553","article-title":"On deciding feature membership in explanations of SDD and related classifiers","author":"Huang","year":"2022","journal-title":"CoRR"},{"key":"B42","unstructured":"2020"},{"key":"B43","doi-asserted-by":"crossref","first-page":"3776","DOI":"10.1609\/aaai.v36i4.20292","article-title":"\u201cUsing MaxSAT for efficient explanations of tree ensembles,\u201d","author":"Ignatiev","year":"2022","journal-title":"AAAI"},{"key":"B44","first-page":"251","article-title":"\u201cSAT-based rigorous explanations for decision lists,\u201d","author":"Ignatiev","year":"2021","journal-title":"SAT"},{"key":"B45","first-page":"335","article-title":"\u201cFrom contrastive to abductive explanations and back again,\u201d","author":"Ignatiev","year":"","journal-title":"AIxIA"},{"key":"B46","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2012.11067","article-title":"On relating \u2018why?' and \u2018why not?' explanations","author":"Ignatiev","year":"","journal-title":"CoRR"},{"key":"B47","first-page":"1511","article-title":"\u201cAbduction-based explanations for machine learning models,\u201d","author":"Ignatiev","year":"","journal-title":"AAAI"},{"key":"B48","first-page":"15857","article-title":"\u201cOn relating explanations and adversarial examples,\u201d","author":"Ignatiev","year":"","journal-title":"NeurIPS"},{"key":"B49","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.1907.02509","article-title":"On validating, repairing and refining heuristic ML explanations","author":"Ignatiev","year":"","journal-title":"CoRR"},{"key":"B50","first-page":"627","article-title":"\u201cA SAT-based approach to learn explainable decision sets,\u201d","author":"Ignatiev","year":"2018","journal-title":"IJCAR"},{"key":"B51","unstructured":"Incremental Decision Tree Induction2020"},{"key":"B52","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2010.1103","article-title":"On explaining decision trees","author":"Izza","year":"2020","journal-title":"CoRR"},{"key":"B53","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1613\/jair.1.13575","article-title":"On tackling explanation redundancy in decision trees","volume":"75","author":"Izza","year":"","journal-title":"J. Artif. Intell. Res"},{"key":"B54","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2106.00546","article-title":"Efficient explanations with relevant sets","author":"Izza","year":"2021","journal-title":"CoRR"},{"key":"B55","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2205.09569","article-title":"Provably precise, succinct and efficient explanations for decision trees","author":"Izza","year":"","journal-title":"CoRR"},{"key":"B56","first-page":"2584","article-title":"\u201cOn explaining random forests with SAT,\u201d","author":"Izza","year":"2021","journal-title":"IJCAI"},{"key":"B57","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2207.04748","article-title":"On computing relevant features for explaining NBCs","author":"Izza","year":"2022","journal-title":"CoRR"},{"key":"B58","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2010.04050","article-title":"A survey of algorithmic recourse: definitions, formulations, solutions, and prospects","author":"Karimi","year":"2020","journal-title":"CoRR"},{"key":"B59","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1145\/3442188.3445899","article-title":"\u201cAlgorithmic recourse: from counterfactual explanations to interventions,\u201d","author":"Karimi","year":"2021","journal-title":"FAccT"},{"key":"B60","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1145\/3065386","article-title":"Imagenet classification with deep convolutional neural networks","volume":"60","author":"Krizhevsky","year":"2017","journal-title":"Commun. ACM"},{"key":"B61","first-page":"1675","article-title":"\u201cInterpretable decision sets: a joint framework for description and prediction,\u201d","author":"Lakkaraju","year":"2016","journal-title":"KDD"},{"key":"B62","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"B63","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1145\/3233231","article-title":"The mythos of model interpretability","volume":"61","author":"Lipton","year":"2018","journal-title":"Commun. ACM"},{"key":"B64","article-title":"\u201cA logic for binary classifiers and their explanation,\u201d","author":"Liu","year":"2021","journal-title":"CLAR"},{"key":"B65","first-page":"158","article-title":"\u201cA logic of \"black box\" classifier systems,\u201d","author":"Liu","year":"","journal-title":"WoLLIC"},{"key":"B66","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-15298-6_10","article-title":"A logic of \"black box\" classifier systems","author":"Liu","year":"","journal-title":"CoRR"},{"key":"B67","first-page":"4765","article-title":"\u201cA unified approach to interpreting model predictions,\u201d","author":"Lundberg","year":"2017","journal-title":"NeurIPS"},{"key":"B68","first-page":"2658","article-title":"\u201cOn guaranteed optimal robust explanations for NLP models,\u201d","author":"Malfa","year":"2021","journal-title":"IJCAI"},{"key":"B69","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2211.00541","article-title":"Logic-based explainability in machine learning","author":"Marques-Silva","year":"2022","journal-title":"CoRR"},{"key":"B70","article-title":"\u201cExplaining naive bayes and other linear classifiers with polynomial time and delay,\u201d","author":"Marques-Silva","year":"2020","journal-title":"NeurIPS"},{"key":"B71","first-page":"7469","article-title":"\u201cExplanations for monotonic classifiers,\u201d","author":"Marques-Silva","year":"2021","journal-title":"ICML"},{"key":"B72","doi-asserted-by":"crossref","first-page":"12342","DOI":"10.1609\/aaai.v36i11.21499","article-title":"\u201cDelivering trustworthy AI through formal XAI,\u201d","author":"Marques-Silva","year":"2022","journal-title":"AAAI"},{"key":"B73","first-page":"4899","article-title":"\u201cReasoning about inconsistent formulas,\u201d","author":"Marques-Silva","year":"2020","journal-title":"IJCAI"},{"key":"B74","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1037\/h0043158","article-title":"The magical number seven, plus or minus two: Some limits on our capacity for processing information","volume":"63","author":"Miller","year":"1956","journal-title":"Psychol. Rev"},{"key":"B75","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.artint.2018.07.007","article-title":"Explanation in artificial intelligence: Insights from the social sciences","volume":"267","author":"Miller","year":"2019","journal-title":"Artif. Intell"},{"key":"B76","unstructured":"MolnarC.\n          Interpretable Machine Learning. Leanpub2020"},{"key":"B77","first-page":"267","article-title":"\u201cAssessing heuristic machine learning explanations with model counting,\u201d","volume-title":"SAT","author":"Narodytska","year":"2019"},{"key":"B78","unstructured":"PennM. L.\n          Penn Machine Learning Benchmarks2020"},{"key":"B79","first-page":"304","article-title":"\u201cGenerating production rules from decision trees,\u201d","volume-title":"IJCAI","author":"Quinlan","year":"1987"},{"key":"B80","doi-asserted-by":"publisher","first-page":"103506","DOI":"10.1016\/j.artint.2021.103506","article-title":"Argumentative explanations for interactive recommendations","volume":"296","author":"Rago","year":"2021","journal-title":"Artif. Intell"},{"key":"B81","first-page":"805","article-title":"\u201cArgumentation as a framework for interactive explanations for recommendations,\u201d","volume-title":"KR","author":"Rago","year":"2020"},{"key":"B82","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/0004-3702(87)90062-2","article-title":"A theory of diagnosis from first principles","volume":"32","author":"Reiter","year":"1987","journal-title":"Artif. Intell"},{"key":"B83","first-page":"1135","article-title":"\u201c\u201cwhy should I trust you?\u201d: explaining the predictions of any classifier,\u201d","volume-title":"KDD","author":"Ribeiro","year":"2016"},{"key":"B84","first-page":"1527","article-title":"\u201cAnchors: high-precision model-agnostic explanations,\u201d","volume-title":"AAAI","author":"Ribeiro","year":"2018"},{"key":"B85","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1038\/s42256-019-0048-x","article-title":"Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead","volume":"1","author":"Rudin","year":"2019","journal-title":"Nat. Mach. Intell"},{"key":"B86","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s43586-022-00172-0","article-title":"Why black box machine learning should be avoided for high-stakes decisions, in brief","volume":"2","author":"Rudin","year":"2022","journal-title":"Nat. Rev. Methods Primers"},{"key":"B87","first-page":"882","article-title":"\u201cOn tractable representations of binary neural networks,\u201d","volume-title":"KR","author":"Shi","year":"2020"},{"key":"B88","first-page":"5103","article-title":"\u201cA symbolic approach to explaining bayesian network classifiers,\u201d","volume-title":"IJCAI","author":"Shih","year":"2018"},{"key":"B89","first-page":"7966","article-title":"\u201cCompiling bayesian network classifiers into decision graphs,\u201d","volume-title":"AAAI","author":"Shih","year":"2019"},{"key":"B90","article-title":"\u201cIntriguing properties of neural networks,\u201d","volume-title":"ICLR","author":"Szegedy","year":"2014"},{"key":"B91","unstructured":"UCI Machine Learning Repository2020"},{"key":"B92","first-page":"10","article-title":"\u201cActionable recourse in linear classification,\u201d","volume-title":"FAT","author":"Ustun","year":"2019"},{"key":"B93","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1023\/A:1007413323501","article-title":"Decision tree induction based on efficient tree restructuring","volume":"29","author":"Utgoff","year":"1997","journal-title":"Mach. Learn"},{"key":"B94","first-page":"284","article-title":"\u201cThe philosophical basis of algorithmic recourse,\u201d","volume-title":"FAT","author":"Venkatasubramanian","year":"2020"},{"key":"B95","volume-title":"Towards Explainable Artificial Intelligence-Interpreting Neural Network Classifiers with Probabilistic Prime Implicants","author":"W\u00e4ldchen","year":"2022"},{"key":"B96","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1613\/jair.1.12359","article-title":"The computational complexity of understanding binary classifier decisions","volume":"70","author":"W\u00e4ldchen","year":"2021","journal-title":"J. Artif. Intell. Res"},{"key":"B97","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1145\/3306618.3314260","article-title":"\u201cA formal approach to explainability,\u201d","volume-title":"AIES","author":"Wolf","year":"2019"},{"key":"B98","article-title":"Eliminating the impossible, whatever remains must be true","author":"Yu","year":"2022","journal-title":"CoRR"}],"container-title":["Frontiers in Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frai.2023.1128212\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T04:31:21Z","timestamp":1682310681000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/frai.2023.1128212\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,24]]},"references-count":98,"alternative-id":["10.3389\/frai.2023.1128212"],"URL":"https:\/\/doi.org\/10.3389\/frai.2023.1128212","relation":{},"ISSN":["2624-8212"],"issn-type":[{"value":"2624-8212","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4,24]]},"article-number":"1128212"}}