Private Synthetic Data Generation in Small Memory

• URL: http://arxiv.org/abs/2412.09756v3
• Date: Wed, 02 Apr 2025 05:01:51 GMT
• Title: Private Synthetic Data Generation in Small Memory
• Authors: Rayne Holland, Seyit Camtepe, Chandra Thapa, Minhui Xue,
• Abstract summary: $mathttPrivHP$ is a lightweight synthetic data generator with textitdifferential privacy guarantees.<n>It balances hierarchy depth, noise addition, and pruning of low-frequency while preserving frequent ones.
• Score: 16.298974544454754
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\Omega = [0,1]$, 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.

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