Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression

Canhong Wen (), Zhenduo Li (), Ruipeng Dong (), Yijin Ni () and Wenliang Pan ()
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Canhong Wen: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
Zhenduo Li: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
Ruipeng Dong: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China
Yijin Ni: Industrial and System Engineering, Georgia Institute of Technology, 30318 Atlanta, Georgia
Wenliang Pan: Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

INFORMS Journal on Computing, 2023, vol. 35, issue 5, 1044-1060

Abstract: Multinomial logistic regression is a useful model for predicting the probabilities of multiclass outcomes. Because of the complexity and high dimensionality of some data, it is challenging to fit a valid model with high accuracy and interpretability. We propose a novel sparse reduced-rank multinomial logistic regression model to jointly select variables and reduce the dimension via a nonconvex row constraint. We develop a block-wise iterative algorithm with a majorizing surrogate function to efficiently solve the optimization problem. From an algorithmic aspect, we show that the output estimator enjoys consistency in estimation and sparsity recovery even in a high-dimensional setting. The finite sample performance of the proposed method is investigated via simulation studies and two real image data sets. The results show that our proposal has competitive performance in both estimation accuracy and computation time.

Keywords: high-dimensional data; multinomial logistic regression; reduced-rank regression; variable selection (search for similar items in EconPapers)
Date: 2023
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