Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation

Mizuho NAGANUMA  Yuichi TAKANO  Ryuhei MIYASHIRO  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E102-D   No.5   pp.1046-1053
Publication Date: 2019/05/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.2018EDP7188
Type of Manuscript: PAPER
Category: Fundamentals of Information Systems
Keyword: 
optimization,  statistics,  feature subset selection,  ordered logit model,  

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Summary: 
This paper is concerned with a mixed-integer optimization (MIO) approach to selecting a subset of relevant features from among many candidates. For ordinal classification, a sequential logit model and an ordered logit model are often employed. For feature subset selection in the sequential logit model, Sato et al.[22] recently proposed a mixed-integer linear optimization (MILO) formulation. In their MILO formulation, a univariate nonlinear function contained in the sequential logit model was represented by a tangent-line-based approximation. We extend this MILO formulation toward the ordered logit model, which is more commonly used for ordinal classification than the sequential logit model is. Making use of tangent planes to approximate a bivariate nonlinear function involved in the ordered logit model, we derive an MILO formulation for feature subset selection in the ordered logit model. Our computational results verify that the proposed method is superior to the L1-regularized ordered logit model in terms of solution quality.