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International Conference on Scalable Uncertainty Management

SUM 2022: Scalable Uncertainty Management pp 295–308Cite as

Explanation of Pseudo-Boolean Functions Using Cooperative Game Theory and Prime Implicants

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13562))

Abstract

Explanation methods can be formal or heuristic-based. Many explanation methods have been developed. Formal methods provide principles to derive sufficient reasons (prime implicants) or necessary reasons (counterfactuals, causes). These approaches are appealing but require to discretize the input and output spaces. Heuristic-based approaches such as feature attribution (such as the Shapley value) work in any condition but the relation to explanation is less clear. We show that they cannot distinguish between conjunction and disjunction, which is not the case with sufficient explanations. This work is an initial work that aims at combining some idea of prime implicants into feature attribution, in order to measure sufficiency of the features. We apply it to two values - the proportional division and the Shapley value.

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Authors and Affiliations

  1. Thales Research and Technology, Palaiseau, France

    Christophe Labreuche

  2. SINCLAIR AI Lab, Palaiseau, France

    Christophe Labreuche

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  1. Christophe Labreuche
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Correspondence to Christophe Labreuche .

Editor information

Editors and Affiliations

  1. IRIT-Université Toulouse, Toulouse, France

    Florence Dupin de Saint-Cyr

  2. Université Paris-Dauphine - PSL, Paris, France

    Meltem Öztürk-Escoffier

  3. Imperial College London, London, UK

    Nico Potyka

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Labreuche, C. (2022). Explanation of Pseudo-Boolean Functions Using Cooperative Game Theory and Prime Implicants. In: Dupin de Saint-Cyr, F., Öztürk-Escoffier, M., Potyka, N. (eds) Scalable Uncertainty Management. SUM 2022. Lecture Notes in Computer Science(), vol 13562. Springer, Cham. https://doi.org/10.1007/978-3-031-18843-5_20

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  • DOI: https://doi.org/10.1007/978-3-031-18843-5_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-18842-8

  • Online ISBN: 978-3-031-18843-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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