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On the Usability of Probably Approximately Correct Implication Bases

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Formal Concept Analysis (ICFCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10308))

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Abstract

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide evidence suggesting that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.

The authors of this work are given in alphabetical order. No priority in authorship is implied.

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Acknowledgments

Daniel Borchmann gratefully acknowledges support by the Cluster of Excellence “Center for Advancing Electronics Dresden” (cfAED). Sergei Obiedkov received support within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE) and within the framework of a subsidy by the Russian Academic Excellence Project ‘5-100’. The computations presented in this paper were conducted by conexp-clj, a general-purpose software for formal concept analysis (https://github.com/exot/conexp-clj).

Author information

Authors and Affiliations

  1. Chair of Automata Theory, Technische Universität Dresden, Dresden, Germany

    Daniel Borchmann

  2. Knowledge and Data Engineering Group, University of Kassel, Kassel, Germany

    Tom Hanika

  3. Interdisciplinary Research Center for Information System Design, University of Kassel, Kassel, Germany

    Tom Hanika

  4. Faculty of Computer Science, National Research University Higher School of Economics, Moscow, Russian Federation

    Sergei Obiedkov

Authors
  1. Daniel Borchmann
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  2. Tom Hanika
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  3. Sergei Obiedkov
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Corresponding author

Correspondence to Daniel Borchmann .

Editor information

Editors and Affiliations

  1. Université de La Rochelle, La Rochelle, France

    Karell Bertet

  2. Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany

    Daniel Borchmann

  3. Université de Rennes, Rennes, France

    Peggy Cellier

  4. Université de Rennes, Rennes, France

    Sébastien Ferré

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Borchmann, D., Hanika, T., Obiedkov, S. (2017). On the Usability of Probably Approximately Correct Implication Bases. In: Bertet, K., Borchmann, D., Cellier, P., Ferré, S. (eds) Formal Concept Analysis. ICFCA 2017. Lecture Notes in Computer Science(), vol 10308. Springer, Cham. https://doi.org/10.1007/978-3-319-59271-8_5

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  • DOI: https://doi.org/10.1007/978-3-319-59271-8_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59270-1

  • Online ISBN: 978-3-319-59271-8

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