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SAT-Based Rigorous Explanations for Decision Lists

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Theory and Applications of Satisfiability Testing – SAT 2021 (SAT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12831))

Abstract

Decision lists (DLs) find a wide range of uses for classification problems in Machine Learning (ML), being implemented in anumber of ML frameworks. DLs are often perceived as interpretable. However, building on recent results for decision trees (DTs), we argue that interpretability is an elusive goal for some DLs. As a result, for some uses of DLs, it will be important to compute (rigorous) explanations. Unfortunately, and in clear contrast with the case of DTs, this paper shows that computing explanations for DLs is computationally hard. Motivated by this result, the paper proposes propositional encodings for computing abductive explanations (AXps) and contrastive explanations (CXps) of DLs. Furthermore, the paper investigates the practical efficiency of a MARCO-like approach for enumerating explanations. The experimental results demonstrate that, for DLs used in practical settings, the use of SAT oracles offers a very efficient solution, and that complete enumeration of explanations is most often feasible.

This work was supported by the AI Interdisciplinary Institute ANITI, funded by the French program “Investing for the Future – PIA3” under Grant agreement no. ANR-19-PI3A-0004, and by the H2020-ICT38 project COALA “Cognitive Assisted agile manufacturing for a Labor force supported by trustworthy Artificial intelligence”.

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Notes

  1. 1.

    Interpretability is a subjective concept, for which no rigorous accepted definition exists [46]. As clarified later in the paper, for a given pair ML model and instance, we equate interpretability with how succinct is the justification for the model’s prediction.

  2. 2.

    The prototype is available at https://github.com/alexeyignatiev/xdl-tool.

  3. 3.

    Recent alternative approaches to sparse decision lists [1, 2, 65] have also been considered but were eventually discarded for two reasons: (1) they can only deal with binary data and (2) they produce sparse decision lists containing a couple of rules and a few literals in total—i.e. these methods do not provide models that would be of interest for our work.

  4. 4.

    https://orangedatamining.com/.

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Author information

Authors and Affiliations

  1. Monash University, Melbourne, Australia

    Alexey Ignatiev

  2. IRIT, CNRS, Toulouse, France

    Joao Marques-Silva

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  1. Alexey Ignatiev
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  2. Joao Marques-Silva
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Correspondence to Alexey Ignatiev .

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Editors and Affiliations

  1. Laboratoire MIS, University of Picardie Jules Verne, Amiens, France

    Chu-Min Li

  2. IIIA-CSIC, Spanish National Research Council (CSIC), Bellaterra, Barcelona, Spain

    Felip Manyà

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Ignatiev, A., Marques-Silva, J. (2021). SAT-Based Rigorous Explanations for Decision Lists. In: Li, CM., Manyà, F. (eds) Theory and Applications of Satisfiability Testing – SAT 2021. SAT 2021. Lecture Notes in Computer Science(), vol 12831. Springer, Cham. https://doi.org/10.1007/978-3-030-80223-3_18

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