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Fast Algorithms for LS and LAD-Collaborative Regression

Author

Listed:
  • Jun Sun

    (School of Science, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, P. R. China)

  • Lingchen Kong

    (School of Science, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, P. R. China)

  • Mei Li

    (School of Science, Beijing Jiaotong University, No. 3 Shangyuancun, Haidian District, Beijing 100044, P. R. China)

Abstract

With the development of modern science and technology, it is easy to obtain a large number of high-dimensional datasets, which are related but different. Classical unimodel analysis is less likely to capture potential links between the different datasets. Recently, a collaborative regression model based on least square (LS) method for this problem has been proposed. In this paper, we propose a robust collaborative regression based on the least absolute deviation (LAD). We give the statistical interpretation of the LS-collaborative regression and LAD-collaborative regression. Then we design an efficient symmetric Gauss–Seidel-based alternating direction method of multipliers algorithm to solve the two models, which has the global convergence and the Q-linear rate of convergence. Finally we report numerical experiments to illustrate the efficiency of the proposed methods.

Suggested Citation

  • Jun Sun & Lingchen Kong & Mei Li, 2022. "Fast Algorithms for LS and LAD-Collaborative Regression," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 39(06), pages 1-29, December.
    • Handle: RePEc:wsi:apjorx:v:39:y:2022:i:06:n:s0217595922500014
    DOI: 10.1142/S0217595922500014
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