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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07035 |
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| _version_ | 1866913646006763520 |
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| author | Wu, Xiaofei Guo, Dingzi Liang, Rongmei Zhang, Zhimin |
| author_facet | Wu, Xiaofei Guo, Dingzi Liang, Rongmei Zhang, Zhimin |
| contents | In the field of high-dimensional data analysis, modeling methods based on quantile loss function are highly regarded due to their ability to provide a comprehensive statistical perspective and effective handling of heterogeneous data. In recent years, many studies have focused on using the parallel alternating direction method of multipliers (P-ADMM) to solve high-dimensional quantile regression and classification problems. One efficient strategy is to reformulate the quantile loss function by introducing slack variables. However, this reformulation introduces a theoretical challenge: even when the regularization term is convex, the convergence of the algorithm cannot be guaranteed. To address this challenge, this paper proposes the Gaussian Back-Substitution strategy, which requires only a simple and effective correction step that can be easily integrated into existing parallel algorithm frameworks, achieving a linear convergence rate. Furthermore, this paper extends the parallel algorithm to handle some novel quantile loss classification models. Numerical simulations demonstrate that the proposed modified P-ADMM algorithm exhibits excellent performance in terms of reliability and efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Parallel ADMM Algorithm with Gaussian Back Substitution for High-Dimensional Quantile Regression and Classification Wu, Xiaofei Guo, Dingzi Liang, Rongmei Zhang, Zhimin Computation In the field of high-dimensional data analysis, modeling methods based on quantile loss function are highly regarded due to their ability to provide a comprehensive statistical perspective and effective handling of heterogeneous data. In recent years, many studies have focused on using the parallel alternating direction method of multipliers (P-ADMM) to solve high-dimensional quantile regression and classification problems. One efficient strategy is to reformulate the quantile loss function by introducing slack variables. However, this reformulation introduces a theoretical challenge: even when the regularization term is convex, the convergence of the algorithm cannot be guaranteed. To address this challenge, this paper proposes the Gaussian Back-Substitution strategy, which requires only a simple and effective correction step that can be easily integrated into existing parallel algorithm frameworks, achieving a linear convergence rate. Furthermore, this paper extends the parallel algorithm to handle some novel quantile loss classification models. Numerical simulations demonstrate that the proposed modified P-ADMM algorithm exhibits excellent performance in terms of reliability and efficiency. |
| title | Parallel ADMM Algorithm with Gaussian Back Substitution for High-Dimensional Quantile Regression and Classification |
| topic | Computation |
| url | https://arxiv.org/abs/2501.07035 |