Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Data

TL;DR

This paper introduces a novel approach to synthetic data generation that balances computational efficiency, privacy guarantees, and data utility by leveraging covariance loss analysis, offering a practical solution to a complex NP-hard problem.

Contribution

It presents a new method that uses covariance loss analysis to produce privacy-preserving synthetic data efficiently with provable guarantees and utility quantification.

Findings

Nearly optimal solutions for covariance loss in conditional expectation.

Constructive methods for microaggregation and synthetic data generation.

Theoretical insights enabling practical privacy-preserving data release.

Abstract

The protection of private information is of vital importance in data-driven research, business, and government. The conflict between privacy and utility has triggered intensive research in the computer science and statistics communities, who have developed a variety of methods for privacy-preserving data release. Among the main concepts that have emerged are anonymity and differential privacy. Today, another solution is gaining traction, synthetic data. However, the road to privacy is paved with NP-hard problems. In this paper we focus on the NP-hard challenge to develop a synthetic data generation method that is computationally efficient, comes with provable privacy guarantees, and rigorously quantifies data utility. We solve a relaxed version of this problem by studying a fundamental, but a first glance completely unrelated, problem in probability concerning the concept of covariance loss. Namely, we find a nearly optimal and constructive answer to the question how much information is lost when we take conditional expectation. Surprisingly, this excursion into theoretical probability produces mathematical techniques that allow us to derive constructive, approximately optimal solutions to difficult applied problems concerning microaggregation, privacy, and synthetic data.