Efficient Sparse Least Absolute Deviation Regression with Differential Privacy
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913183240814592 |
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| author | Liu, Weidong Mao, Xiaojun Zhang, Xiaofei Zhang, Xin |
| author_facet | Liu, Weidong Mao, Xiaojun Zhang, Xiaofei Zhang, Xin |
| contents | In recent years, privacy-preserving machine learning algorithms have attracted increasing attention because of their important applications in many scientific fields. However, in the literature, most privacy-preserving algorithms demand learning objectives to be strongly convex and Lipschitz smooth, which thus cannot cover a wide class of robust loss functions (e.g., quantile/least absolute loss). In this work, we aim to develop a fast privacy-preserving learning solution for a sparse robust regression problem. Our learning loss consists of a robust least absolute loss and an $\ell_1$ sparse penalty term. To fast solve the non-smooth loss under a given privacy budget, we develop a Fast Robust And Privacy-Preserving Estimation (FRAPPE) algorithm for least absolute deviation regression. Our algorithm achieves a fast estimation by reformulating the sparse LAD problem as a penalized least square estimation problem and adopts a three-stage noise injection to guarantee the $(ε,δ)$-differential privacy. We show that our algorithm can achieve better privacy and statistical accuracy trade-off compared with the state-of-the-art privacy-preserving regression algorithms. In the end, we conduct experiments to verify the efficiency of our proposed FRAPPE algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Sparse Least Absolute Deviation Regression with Differential Privacy Liu, Weidong Mao, Xiaojun Zhang, Xiaofei Zhang, Xin Machine Learning Methodology 62J07 In recent years, privacy-preserving machine learning algorithms have attracted increasing attention because of their important applications in many scientific fields. However, in the literature, most privacy-preserving algorithms demand learning objectives to be strongly convex and Lipschitz smooth, which thus cannot cover a wide class of robust loss functions (e.g., quantile/least absolute loss). In this work, we aim to develop a fast privacy-preserving learning solution for a sparse robust regression problem. Our learning loss consists of a robust least absolute loss and an $\ell_1$ sparse penalty term. To fast solve the non-smooth loss under a given privacy budget, we develop a Fast Robust And Privacy-Preserving Estimation (FRAPPE) algorithm for least absolute deviation regression. Our algorithm achieves a fast estimation by reformulating the sparse LAD problem as a penalized least square estimation problem and adopts a three-stage noise injection to guarantee the $(ε,δ)$-differential privacy. We show that our algorithm can achieve better privacy and statistical accuracy trade-off compared with the state-of-the-art privacy-preserving regression algorithms. In the end, we conduct experiments to verify the efficiency of our proposed FRAPPE algorithm. |
| title | Efficient Sparse Least Absolute Deviation Regression with Differential Privacy |
| topic | Machine Learning Methodology 62J07 |
| url | https://arxiv.org/abs/2401.01294 |