### 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 language | English |
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Title of host publication | Mathematical Software - 5th International Conference, ICMS 2016, Proceedings |

Editors | Gert-Martin Greuel, Andrew Sommese, Thorsten Koch, Peter Paule |

Publisher | Springer Verlag |

Pages | 292-300 |

Number of pages | 9 |

ISBN (Print) | 9783319424316 |

DOIs | |

Publication status | Published - Jan 1 2016 |

Event | 5th International Conference on Mathematical Software, ICMS 2016 - Berlin, Germany Duration: Jul 11 2016 → Jul 14 2016 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9725 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 5th International Conference on Mathematical Software, ICMS 2016 |
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Country | Germany |

City | Berlin |

Period | 7/11/16 → 7/14/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Mixed integer nonlinear program for minimization of Akaike’s information criterion

AU - Kimura, Keiji

AU - Waki, Hayato

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84978811411&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978811411&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42432-3_36

DO - 10.1007/978-3-319-42432-3_36

M3 - Conference contribution

AN - SCOPUS:84978811411

SN - 9783319424316

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 292

EP - 300

BT - Mathematical Software - 5th International Conference, ICMS 2016, Proceedings

A2 - Greuel, Gert-Martin

A2 - Sommese, Andrew

A2 - Koch, Thorsten

A2 - Paule, Peter

PB - Springer Verlag

ER -