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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2409.04636 |
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| _version_ | 1866929490735661056 |
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| author | Kalinin, Nikita P. |
| author_facet | Kalinin, Nikita P. |
| contents | In these notes, we prove a recent conjecture posed in the paper by Räisä, O. et al. [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimization (2024)]. Theorem 6.2 of the paper asserts that for the Sampled Gaussian Mechanism - a composition of subsampling and additive Gaussian noise, the effective noise level, $σ_{\text{eff}} = \frac{σ(q)}{q}$, decreases as a function of the subsampling rate $q$. Consequently, larger subsampling rates are preferred for better privacy-utility trade-offs. Our notes provide a rigorous proof of Conjecture 6.3, which was left unresolved in the original paper, thereby completing the proof of Theorem 6.2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Notes on Sampled Gaussian Mechanism Kalinin, Nikita P. Machine Learning In these notes, we prove a recent conjecture posed in the paper by Räisä, O. et al. [Subsampling is not Magic: Why Large Batch Sizes Work for Differentially Private Stochastic Optimization (2024)]. Theorem 6.2 of the paper asserts that for the Sampled Gaussian Mechanism - a composition of subsampling and additive Gaussian noise, the effective noise level, $σ_{\text{eff}} = \frac{σ(q)}{q}$, decreases as a function of the subsampling rate $q$. Consequently, larger subsampling rates are preferred for better privacy-utility trade-offs. Our notes provide a rigorous proof of Conjecture 6.3, which was left unresolved in the original paper, thereby completing the proof of Theorem 6.2. |
| title | Notes on Sampled Gaussian Mechanism |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2409.04636 |