Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Model
Abstract
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between the logistic loss function and its quadratic approximation, their formulation may fail to find a good subset of features. To overcome this drawback, we apply a piecewise-linear approximation to the logistic loss function. Accordingly, we frame the feature subset selection problem of minimizing an information criterion as a mixed integer linear optimization problem. The computational results demonstrate that our piecewise-linear approximation approach found a better subset of features than the quadratic approximation approach.
Cite
@article{arxiv.1510.05417,
title = {Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Model},
author = {Toshiki Sato and Yuichi Takano and Ryuhei Miyashiro},
journal= {arXiv preprint arXiv:1510.05417},
year = {2015}
}