This repository contains the companion iPython notebook and datasets for the paper on Shapley and Banzhaf vectors of a formal concept prepared for CLA 2020 by Dmitry Ignatov and Leonard Kwuida. It proposes interpretable contribution of attributes to concept stability values:

• Dmitry I. Ignatov, Léonard Kwuida: Shapley and Banzhaf Vectors of a Formal Concept. CLA 2020: 259-271.

Abstract

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 count- ing 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.

There is also our work on Shapley values for rule-based (classification) JSM-method in terms of Concept Lattices (FCA) presented in the paper:

• Dmitry I. Ignatov, Léonard Kwuida: Interpretable Concept-Based Classification with Shapley Values. ICCS 2020: 90-102.

The associated repository also contains a demo code and data: https://github.com/dimachine/Shap4JSM/.

To acknowledge use of the code and data in publications, please cite the following papers and mention this repository.

@inproceedings{Ignatov:2020a,
  author    = {Dmitry I. Ignatov and
               L{\'{e}}onard Kwuida},
  editor    = {Francisco J. Valverde{-}Albacete and
               Martin Trnecka},
  title     = {Shapley and Banzhaf Vectors of a Formal Concept},
  booktitle = {Proceedings of the Fifthteenth International Conference on Concept
               Lattices and Their Applications, Tallinn, Estonia, June 29-July 1,
               2020},
  series    = {{CEUR} Workshop Proceedings},
  volume    = {2668},
  pages     = {259--271},
  publisher = {CEUR-WS.org},
  year      = {2020},
  url       = {http://ceur-ws.org/Vol-2668/paper20.pdf},
}

@inproceedings{Ignatov:2020b,
  author    = {Dmitry I. Ignatov and
               L{\'{e}}onard Kwuida},
  editor    = {Mehwish Alam and
               Tanya Braun and
               Bruno Yun},
  title     = {Interpretable Concept-Based Classification with Shapley Values},
  booktitle = {Ontologies and Concepts in Mind and Machine - 25th International Conference
               on Conceptual Structures, {ICCS} 2020, Bolzano, Italy, September 18-20,
               2020, Proceedings},
  series    = {Lecture Notes in Computer Science},
  volume    = {12277},
  pages     = {90--102},
  publisher = {Springer},
  year      = {2020},
  url       = {https://doi.org/10.1007/978-3-030-57855-8\_7},
  doi       = {10.1007/978-3-030-57855-8\_7},
}

#Interpretable Machine Learning

#Stability

#Shapley value

#Banzhaf index

#Penrose index

#Formal Concept Analysis