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A highly efficient ADMM-based algorithm for outlier-robust regression with Huber loss

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Abstract

Huber robust regression (HRR) has attracted much attention in machine learning due to its greater robustness to outliers compared to least-squares regression. However, existing algorithms for HRR are computationally much less efficient than those for least-squares regression. Based on a maximally split alternating direction method of multipliers (MS-ADMM) for model fitting, a highly computationally efficient algorithm referred to as the modified MS-ADMM is derived in this article for HRR. After analyzing the convergence of the modified MS-ADMM, a parameter selection scheme is presented for the algorithm. With the parameter values calculated via this scheme, the modified MS-ADMM converges very rapidly, much faster than several typical HRR algorithms. Through applications in the training of stochastic neural networks and comparisons with existing algorithms, the modified MS-ADMM is shown to be computationally much more efficient than the convex quadratic programming method, the Newton method, the iterative reweighted least-squares method, and Nesterov’s accelerated gradient method. Implementation of the proposed algorithm on a GPU-based parallel computing platform demonstrates its higher GPU acceleration ratio compared to the competing methods and, thus, its greater superiority in computational efficiency over the competing methods.

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All the data used in this article are sourced from open and publicly accessible platforms. No proprietary, confidential, or private data has been used.

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Acknowledgements

This work was supported by the Natural Science Foundation of Zhejiang Province (LZ22F030002, LZ24F030010), the National Natural Science Foundation of China (U1909209), the National Key Research Program of China (2021YFE0100100), and the Research Funding of Education of Zhejiang Province (Y202249784).

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Authors and Affiliations

  1. Artificial Intelligence Institute, Hangzhou Dianzi University, Hangzhou, 310018, China

    Tianlei Wang, Xiaoping Lai & Jiuwen Cao

  2. Machine Learning and I-Health International Cooperation Base of Zhejiang Province, Hangzhou Dianzi University, Hangzhou, 310018, China

    Tianlei Wang, Xiaoping Lai & Jiuwen Cao

Authors
  1. Tianlei Wang
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  2. Xiaoping Lai
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  3. Jiuwen Cao
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Contributions

Tianlei Wang: Conceptualization, Investigation, Writing—review and editing. Xiaoping Lai: Conceptualization, Methodology, Software, Investigation, Writing—original draft preparation. Jiuwen Cao: Conceptualization, Investigation, Writing—review and editing, Supervision.

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Correspondence to Jiuwen Cao.

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Wang, T., Lai, X. & Cao, J. A highly efficient ADMM-based algorithm for outlier-robust regression with Huber loss. Appl Intell 54, 5147–5166 (2024). https://doi.org/10.1007/s10489-024-05370-9

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