TY - GEN

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

AU - Kimura, Keiji

AU - Waki, Hayato

PY - 2016

Y1 - 2016

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

T2 - 5th International Conference on Mathematical Software, ICMS 2016

Y2 - 11 July 2016 through 14 July 2016

ER -