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 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
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 proceeding › Conference contribution
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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 -