Shapley and Banzhaf Vectors of a Formal Concept

Ignatov, Dmitry I.; Kwuida, Léonard (2020). Shapley and Banzhaf Vectors of a Formal Concept In: International Conference on Concept Lattices and Their Applications. CEUR Workshop Proceedings: Vol. 2668 (pp. 259-271). CEUR-WS.org

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We propose the usage of two power indices from cooperative game theory and public choice theory for ranking attributes of closed sets, namely intents of formal concepts (or closed itemsets). The introduced indices are related to extensional concept stability and based on counting generators, especially those that contain a selected attribute. The introduction of such indices is motivated by the so-called interpretable machine learning, which supposes that we do not only have the class membership decision of a trained model for a particular object, but also a set of attributes (in the form of JSM-hypotheses or other patterns) along with individual importance of their single attributes (or more complex constituent elements). We characterise computation of Shapley and Banzhaf values of a formal concept in terms of minimal generators and their order filters, provide the reader with their properties important for computation purposes, and show experimental results.

Item Type:	Conference or Workshop Item (Paper)
Division/Institute:	Business School > Business Foundations and Methods
Name:	Ignatov, Dmitry I. and Kwuida, Léonard0000-0002-9811-0747
Series:	CEUR Workshop Proceedings
Publisher:	CEUR-WS.org
Language:	English
Submitter:	Léonard Kwuida
Date Deposited:	01 Oct 2020 15:03
Last Modified:	21 Sep 2021 02:18
Uncontrolled Keywords:	Shapley value, Banzhaf value, Interpretable Machine Learning, formal concepts, closed itemsets
ARBOR DOI:	10.24451/arbor.12975
URI:	https://arbor.bfh.ch/id/eprint/12975