Mixed integer nonlinear program for minimization of Akaike’s information criterion

Keiji Kimura, Hayato Waki

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    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-andbound 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.

    Original languageEnglish
    Title of host publicationMathematical Software - 5th International Conference, ICMS 2016, Proceedings
    EditorsGert-Martin Greuel, Andrew Sommese, Thorsten Koch, Peter Paule
    PublisherSpringer Verlag
    Pages292-300
    Number of pages9
    ISBN (Print)9783319424316
    DOIs
    Publication statusPublished - Jan 1 2016
    Event5th International Conference on Mathematical Software, ICMS 2016 - Berlin, Germany
    Duration: Jul 11 2016Jul 14 2016

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume9725
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other5th International Conference on Mathematical Software, ICMS 2016
    CountryGermany
    CityBerlin
    Period7/11/167/14/16

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    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Kimura, K., & Waki, H. (2016). Mixed integer nonlinear program for minimization of Akaike’s information criterion. In G-M. Greuel, A. Sommese, T. Koch, & P. Paule (Eds.), Mathematical Software - 5th International Conference, ICMS 2016, Proceedings (pp. 292-300). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9725). Springer Verlag. https://doi.org/10.1007/978-3-319-42432-3_36