### 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 |
---|---|

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) |
---|---|

Volume | 9725 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

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

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