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Computing Optimal Decision Sets with SAT

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Book cover Principles and Practice of Constraint Programming (CP 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12333))

Abstract

As machine learning is increasingly used to help make decisions, there is a demand for these decisions to be explainable. Arguably, the most explainable machine learning models use decision rules. This paper focuses on decision sets, a type of model with unordered rules, which explains each prediction with a single rule. In order to be easy for humans to understand, these rules must be concise. Earlier work on generating optimal decision sets first minimizes the number of rules, and then minimizes the number of literals, but the resulting rules can often be very large. Here we consider a better measure, namely the total size of the decision set in terms of literals. So we are not driven to a small set of rules which require a large number of literals. We provide the first approach to determine minimum-size decision sets that achieve minimum empirical risk and then investigate sparse alternatives where we trade accuracy for size. By finding optimal solutions we show we can build decision set classifiers that are almost as accurate as the best heuristic methods, but far more concise, and hence more explainable.

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Notes

  1. 1.

    https://www.starexec.org/.

  2. 2.

    The prototype adapts all the developed models to the case of multiple classes, which is motivated by the practical importance of non-binary classification.

  3. 3.

    This average value is the highest possible accuracy that can be achieved on these datasets whatever machine learning model is considered.

  4. 4.

    In a unit-size decision set, the literal is meant to assign a constant class. This can be seen as applying a default rule.

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Acknowledgments

This work is partially supported by the Australian Research Council through Discovery Grant DP170103174.

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Authors and Affiliations

  1. Faculty of Information Technology, Monash University, Melbourne, Australia

    Jinqiang Yu, Alexey Ignatiev, Peter J. Stuckey & Pierre Le Bodic

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  1. Jinqiang Yu
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  2. Alexey Ignatiev
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  4. Pierre Le Bodic
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Correspondence to Alexey Ignatiev .

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  1. Insight Centre for Data Analytics, School for Computer Science and Information Technology, University College Cork, Cork, Ireland

    Helmut Simonis

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Yu, J., Ignatiev, A., Stuckey, P.J., Le Bodic, P. (2020). Computing Optimal Decision Sets with SAT. In: Simonis, H. (eds) Principles and Practice of Constraint Programming. CP 2020. Lecture Notes in Computer Science(), vol 12333. Springer, Cham. https://doi.org/10.1007/978-3-030-58475-7_55

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  • DOI: https://doi.org/10.1007/978-3-030-58475-7_55

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