Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Model

Toshiki Sato; Yuichi Takano; Ryuhei Miyashiro

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arXiv · 1510.05417

Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Model

Toshiki Sato·Yuichi Takano·Ryuhei Miyashiro

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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.

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BibTeX RIS

Toshiki Sato, Yuichi Takano, Ryuhei Miyashiro. 2015-10-19. Piecewise-Linear Approximation for Feature Subset Selection in a Sequential Logit Model. https://arxiv.org/abs/1510.05417

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