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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/2504.16535 |
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| _version_ | 1866913805547601920 |
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| author | Xiao, Peiwen Liu, Xiaohui Pan, Guangming Long, Wei |
| author_facet | Xiao, Peiwen Liu, Xiaohui Pan, Guangming Long, Wei |
| contents | In this paper, we introduce a novel decentralized surrogate gradient-based algorithm for quantile regression in a feature-distributed setting, where global features are dispersed across multiple machines within a decentralized network. The proposed algorithm, \texttt{DSG-cqr}, utilizes a convolution-type smoothing approach to address the non-smooth nature of the quantile loss function. \texttt{DSG-cqr} is fully decentralized, conjugate-free, easy to implement, and achieves linear convergence up to statistical precision. To ensure privacy, we adopt the Gaussian mechanism to provide $(ε,δ)$-differential privacy. To overcome the exact residual calculation problem, we estimate residuals using auxiliary variables and develop a confidence interval construction method based on Wald statistics. Theoretical properties are established, and the practical utility of the methods is also demonstrated through extensive simulations and a real-world data application. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decentralized Quantile Regression for Feature-Distributed Massive Datasets with Privacy Guarantees Xiao, Peiwen Liu, Xiaohui Pan, Guangming Long, Wei Computation In this paper, we introduce a novel decentralized surrogate gradient-based algorithm for quantile regression in a feature-distributed setting, where global features are dispersed across multiple machines within a decentralized network. The proposed algorithm, \texttt{DSG-cqr}, utilizes a convolution-type smoothing approach to address the non-smooth nature of the quantile loss function. \texttt{DSG-cqr} is fully decentralized, conjugate-free, easy to implement, and achieves linear convergence up to statistical precision. To ensure privacy, we adopt the Gaussian mechanism to provide $(ε,δ)$-differential privacy. To overcome the exact residual calculation problem, we estimate residuals using auxiliary variables and develop a confidence interval construction method based on Wald statistics. Theoretical properties are established, and the practical utility of the methods is also demonstrated through extensive simulations and a real-world data application. |
| title | Decentralized Quantile Regression for Feature-Distributed Massive Datasets with Privacy Guarantees |
| topic | Computation |
| url | https://arxiv.org/abs/2504.16535 |