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Mixed Integer Nonlinear Program for Minimization of Akaike’s Information Criterion

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Book cover Mathematical Software – ICMS 2016 (ICMS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9725))

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Abstract

Akaike’s information criterion (AIC) is a measure of the quality of a statistical model for a given set of data. We can determine the best statistical model for a particular data set by the minimization based on the AIC. Since it is difficult to find the best statistical model from a set of candidates by this minimization in practice, stepwise methods, which are local search algorithms, are commonly used to find a better statistical model though it may not be the best.

We formulate this AIC minimization as a mixed integer nonlinear programming problem and propose a method to find the best statistical model. In particular, we propose ways to find lower and upper bounds and a branching rule for this minimization. We then combine them with SCIP, which is a mathematical optimization software and a branch-and-bound framework. We show that the proposed method can provide the best statistical model based on AIC for small-sized or medium-sized benchmark data sets in UCI Machine Learning Repository. Furthermore, we show that this method can find good quality solutions for large-sized benchmark data sets.

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Acknowledgements

The second author was supported by JSPS KAKENHI Grant Numbers 26400203. We would like to thank the anonymous referees for providing significant comments on the presentation of the manuscript.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, Japan

    Keiji Kimura

  2. Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan

    Hayato Waki

Authors
  1. Keiji Kimura
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  2. Hayato Waki
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Corresponding author

Correspondence to Keiji Kimura .

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Editors and Affiliations

  1. Universität Kaiserslautern , Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Zuse Institute Berlin , Berlin, Germany

    Thorsten Koch

  3. Johannes Kepler University Linz , Hagenberg, Austria

    Peter Paule

  4. University of Notre Dame , Notre Dame, Indiana, USA

    Andrew Sommese

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© 2016 Springer International Publishing Switzerland

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Kimura, K., Waki, H. (2016). Mixed Integer Nonlinear Program for Minimization of Akaike’s Information Criterion. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_36

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  • DOI: https://doi.org/10.1007/978-3-319-42432-3_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42431-6

  • Online ISBN: 978-3-319-42432-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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