Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916839052804096 |
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| author | Cai, T. Tony Wang, Yichen Zhang, Linjun |
| author_facet | Cai, T. Tony Wang, Yichen Zhang, Linjun |
| contents | Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and non-parametric regression over the Sobolev class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07152 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning Cai, T. Tony Wang, Yichen Zhang, Linjun Statistics Theory Cryptography and Security Machine Learning Methodology Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and non-parametric regression over the Sobolev class. |
| title | Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning |
| topic | Statistics Theory Cryptography and Security Machine Learning Methodology |
| url | https://arxiv.org/abs/2303.07152 |