PREM: Privately Answering Statistical Queries with Relative Error

• URL: http://arxiv.org/abs/2502.14809v1
• Date: Thu, 20 Feb 2025 18:32:02 GMT
• Title: PREM: Privately Answering Statistical Queries with Relative Error
• Authors: Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, Pasin Manurangsi, Sushant Sachdeva,
• Abstract summary: We introduce $mathsfPREM$ (Private Relative Error Multiplicative weight update), a new framework for generating synthetic data that a relative error guarantee for statistical queries under $(varepsilon, delta)$ differential privacy (DP) We complement our algorithm with nearly matching lower bounds.
• Score: 91.98332694700046
• License:
• Abstract: We introduce $\mathsf{PREM}$ (Private Relative Error Multiplicative weight update), a new framework for generating synthetic data that achieves a relative error guarantee for statistical queries under $(\varepsilon, \delta)$ differential privacy (DP). Namely, for a domain ${\cal X}$, a family ${\cal F}$ of queries $f : {\cal X} \to \{0, 1\}$, and $\zeta > 0$, our framework yields a mechanism that on input dataset $D \in {\cal X}^n$ outputs a synthetic dataset $\widehat{D} \in {\cal X}^n$ such that all statistical queries in ${\cal F}$ on $D$, namely $\sum_{x \in D} f(x)$ for $f \in {\cal F}$, are within a $1 \pm \zeta$ multiplicative factor of the corresponding value on $\widehat{D}$ up to an additive error that is polynomial in $\log |{\cal F}|$, $\log |{\cal X}|$, $\log n$, $\log(1/\delta)$, $1/\varepsilon$, and $1/\zeta$. In contrast, any $(\varepsilon, \delta)$-DP mechanism is known to require worst-case additive error that is polynomial in at least one of $n, |{\cal F}|$, or $|{\cal X}|$. We complement our algorithm with nearly matching lower bounds.

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