Minimax density estimation in the adversarial framework under local differential privacy
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909692107685888 |
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| author | Albert, Mélisande Chevallier, Juliette Laurent, Béatrice Sacko, Ousmane |
| author_facet | Albert, Mélisande Chevallier, Juliette Laurent, Béatrice Sacko, Ousmane |
| contents | We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates over Sobolev spaces under local differential privacy. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates. Finally, we develop an adaptive procedure which is optimal in the minimax sense up to logarithmic terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimax density estimation in the adversarial framework under local differential privacy Albert, Mélisande Chevallier, Juliette Laurent, Béatrice Sacko, Ousmane Statistics Theory We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates over Sobolev spaces under local differential privacy. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates. Finally, we develop an adaptive procedure which is optimal in the minimax sense up to logarithmic terms. |
| title | Minimax density estimation in the adversarial framework under local differential privacy |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2403.18357 |