Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets

TL;DR

This paper introduces a differentially private algorithm that efficiently generates low-dimensional synthetic data from high-dimensional datasets, overcoming the curse of dimensionality with a utility guarantee based on Wasserstein distance.

Contribution

It presents a novel private PCA method with near-optimal accuracy that does not require a spectral gap, enabling better synthetic data generation from high-dimensional data.

Findings

Achieves utility guarantees for synthetic data with respect to Wasserstein distance.

Provides a private PCA algorithm with near-optimal accuracy without spectral gap assumptions.

Effectively mitigates the curse of dimensionality in differentially private data synthesis.

Abstract

Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix.