Chinese Quarterly Journal of Mathematics ›› 2021, Vol. 36 ›› Issue (3): 275-287.doi: 10.13371/j.cnki.chin.q.j.m.2021.03.006

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Sparse Reduced-Rank Regression with Outlier Detection

  

  1. School of Data Science, University of Science and Technology of China
  • Received:2021-04-22 Online:2021-09-30 Published:2021-10-08
  • Contact: LIANG Bing-jie (1997-), female, native of Zhengzhou, Henan, master of University of Science and Technology of China, engages in Statistics.
  • About author: LIANG Bing-jie (1997-), female, native of Zhengzhou, Henan, master of University of Science and Technology of China, engages in Statistics.

Abstract:  Based on the multivariate mean-shift regression model, we propose a new
sparse reduced-rank regression approach to achieve low-rank sparse estimation and outlier
detection simultaneously. A sparse mean-shift matrix is introduced in the model to indicate
outliers. The rank constraint and the group-lasso type penalty for the coefficient matrix
encourage the low-rank row sparse structure of coefficient matrix and help to achieve
dimension reduction and variable selection. An algorithm is developed for solving our
problem. In our simulation and real-data application, our new method shows competitive
performance compared to other methods.

Key words:  Reduced-rank regression, Sparsity, Outlier detection, Group-lasso type penalty

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