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Online Differentially Private Synthetic Data Generation

Yiyun He, Roman Vershynin, Yizhe Zhu

TL;DR

An online algorithm that generates a differentially private synthetic dataset at each time with a near-optimal accuracy bound and requires only an extra polylog factor in the accuracy bound is developed.

Abstract

We present a polynomial-time algorithm for online differentially private synthetic data generation. For a data stream within the hypercube $[0,1]^d$ and an infinite time horizon, we develop an online algorithm that generates a differentially private synthetic dataset at each time $t$. This algorithm achieves a near-optimal accuracy bound of $O(\log(t)t^{-1/d})$ for $d\geq 2$ and $O(\log^{4.5}(t)t^{-1})$ for $d=1$ in the 1-Wasserstein distance. This result extends the previous work on the continual release model for counting queries to Lipschitz queries. Compared to the offline case, where the entire dataset is available at once, our approach requires only an extra polylog factor in the accuracy bound.

Online Differentially Private Synthetic Data Generation

TL;DR

An online algorithm that generates a differentially private synthetic dataset at each time with a near-optimal accuracy bound and requires only an extra polylog factor in the accuracy bound is developed.

Abstract

We present a polynomial-time algorithm for online differentially private synthetic data generation. For a data stream within the hypercube and an infinite time horizon, we develop an online algorithm that generates a differentially private synthetic dataset at each time . This algorithm achieves a near-optimal accuracy bound of for and for in the 1-Wasserstein distance. This result extends the previous work on the continual release model for counting queries to Lipschitz queries. Compared to the offline case, where the entire dataset is available at once, our approach requires only an extra polylog factor in the accuracy bound.
Paper Structure (23 sections, 10 theorems, 53 equations, 4 algorithms)

This paper contains 23 sections, 10 theorems, 53 equations, 4 algorithms.

Table of Contents

  1. Introduction
  2. Continual release model
  3. Differentially private synthetic data
  4. Main results
  5. Comparison to previous results
  6. Organization of the paper
  7. Preliminaries
  8. Differential privacy
  9. Online synthetic data generation
  10. Wasserstein distance
  11. Integer Laplacian distribution
  12. Online synthetic data
  13. Binary partition
  14. Main algorithm
  15. Sparse counting algorithm from dwork2015pure
  16. ...and 8 more sections

Key Result

Theorem 1.1

For any constant $\varepsilon>0$, there is an $\varepsilon$-differentially private algorithm such that, for any data stream $x_1,\dots,x_t,\dots \in [0,1]^d$, at any time $t$, it transforms the first $t$ points $\mathcal{X}_t=\{x_1,\dots,x_t\}$ into $t$ points $\mathcal{Y}_t\subset [0,1]^d$, with th where $W_1(\mu_{\mathcal{X}_t},\mu_{\mathcal{Y}_t})$ is the 1-Wasserstein distance between two empi

Theorems & Definitions (21)

  • Theorem 1.1: Online DP synthetic data
  • Remark 1.2
  • Definition 2.1: Neighboring datasets
  • Definition 2.2: Differential Privacy
  • Lemma 3.1
  • Lemma 3.2
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • ...and 11 more