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

Fingerprint

Information Criterion
Statistical Model
Integer
Benchmark
Branching Rules
Mixed Integer Nonlinear Programming
Local Search Algorithm
Nonlinear programming
Repository
Learning systems
Statistical Models
Upper and Lower Bounds
Machine Learning
Branch
Model-based
Software
Optimization

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

Mixed integer nonlinear program for minimization of Akaike’s information criterion. / Kimura, Keiji; Waki, Hayato.

Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. ed. / Gert-Martin Greuel; Andrew Sommese; Thorsten Koch; Peter Paule. Springer Verlag, 2016. p. 292-300 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9725).

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

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9725, Springer Verlag, pp. 292-300, 5th International Conference on Mathematical Software, ICMS 2016, Berlin, Germany, 7/11/16. https://doi.org/10.1007/978-3-319-42432-3_36
Kimura K, Waki H. Mixed integer nonlinear program for minimization of Akaike’s information criterion. In Greuel G-M, Sommese A, Koch T, Paule P, editors, Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. Springer Verlag. 2016. p. 292-300. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-42432-3_36
Kimura, Keiji ; Waki, Hayato. / Mixed integer nonlinear program for minimization of Akaike’s information criterion. Mathematical Software - 5th International Conference, ICMS 2016, Proceedings. editor / Gert-Martin Greuel ; Andrew Sommese ; Thorsten Koch ; Peter Paule. Springer Verlag, 2016. pp. 292-300 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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