Private Synthetic Data Generation in Bounded Memory
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866911308787482624 |
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| author | Holland, Rayne Camtepe, Seyit Thapa, Chandra Xue, Minhui |
| author_facet | Holland, Rayne Camtepe, Seyit Thapa, Chandra Xue, Minhui |
| contents | We propose $\mathtt{PrivHP}$, a lightweight synthetic data generator with \textit{differential privacy} guarantees. $\mathtt{PrivHP}$ uses a novel hierarchical decomposition that approximates the input's cumulative distribution function (CDF) in bounded memory. It balances hierarchy depth, noise addition, and pruning of low-frequency subdomains while preserving frequent ones. Private sketches estimate subdomain frequencies efficiently without full data access.
A key feature is the pruning parameter $k$, which controls the trade-off between space and utility. We define the skew measure $\mathtt{tail}_k$, capturing all but the top $k$ subdomain frequencies. Given a dataset $\mathcal{X}$, $\mathtt{PrivHP}$ uses $M=\mathcal{O}(k\log^2 |X|)$ space and, for input domain $Ω= [0,1]$, ensures $\varepsilon$-differential privacy. It yields a generator with expected Wasserstein distance: \[ \mathcal{O}\left(\frac{\log^2 M}{\varepsilon n} + \frac{||\mathtt{tail}_k(\mathcal{X})||_1}{M n}\right) \] from the empirical distribution. This parameterized trade-off offers a level of flexibility unavailable in prior work. We also provide interpretable utility bounds that account for hierarchy depth, privacy noise, pruning, and frequency estimation errors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Private Synthetic Data Generation in Bounded Memory Holland, Rayne Camtepe, Seyit Thapa, Chandra Xue, Minhui Cryptography and Security Data Structures and Algorithms We propose $\mathtt{PrivHP}$, a lightweight synthetic data generator with \textit{differential privacy} guarantees. $\mathtt{PrivHP}$ uses a novel hierarchical decomposition that approximates the input's cumulative distribution function (CDF) in bounded memory. It balances hierarchy depth, noise addition, and pruning of low-frequency subdomains while preserving frequent ones. Private sketches estimate subdomain frequencies efficiently without full data access. A key feature is the pruning parameter $k$, which controls the trade-off between space and utility. We define the skew measure $\mathtt{tail}_k$, capturing all but the top $k$ subdomain frequencies. Given a dataset $\mathcal{X}$, $\mathtt{PrivHP}$ uses $M=\mathcal{O}(k\log^2 |X|)$ space and, for input domain $Ω= [0,1]$, ensures $\varepsilon$-differential privacy. It yields a generator with expected Wasserstein distance: \[ \mathcal{O}\left(\frac{\log^2 M}{\varepsilon n} + \frac{||\mathtt{tail}_k(\mathcal{X})||_1}{M n}\right) \] from the empirical distribution. This parameterized trade-off offers a level of flexibility unavailable in prior work. We also provide interpretable utility bounds that account for hierarchy depth, privacy noise, pruning, and frequency estimation errors. |
| title | Private Synthetic Data Generation in Bounded Memory |
| topic | Cryptography and Security Data Structures and Algorithms |
| url | https://arxiv.org/abs/2412.09756 |