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.
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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 -