Nonparametric extensions of randomized response for private confidence sets
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911965792698368 |
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| author | Waudby-Smith, Ian Wu, Zhiwei Steven Ramdas, Aaditya |
| author_facet | Waudby-Smith, Ian Wu, Zhiwei Steven Ramdas, Aaditya |
| contents | This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ with mean $μ^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $μ^\star$ when only given access to the privatized data. To achieve this, we study a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response'' mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_08728 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonparametric extensions of randomized response for private confidence sets Waudby-Smith, Ian Wu, Zhiwei Steven Ramdas, Aaditya Methodology Cryptography and Security Statistics Theory Machine Learning This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ with mean $μ^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $μ^\star$ when only given access to the privatized data. To achieve this, we study a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response'' mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests. |
| title | Nonparametric extensions of randomized response for private confidence sets |
| topic | Methodology Cryptography and Security Statistics Theory Machine Learning |
| url | https://arxiv.org/abs/2202.08728 |