Private measures, random walks, and synthetic data

TL;DR

This paper introduces a polynomial-time method for creating private measures and synthetic data under metric privacy, enabling accurate statistical analysis and addressing limitations of traditional differential privacy mechanisms.

Contribution

It develops a new algorithm for private measures and synthetic data using metric privacy, with theoretical guarantees and a novel superregular random walk construction.

Findings

Provides utility guarantees for complex machine learning tasks.

Proves an asymptotically sharp min-max result for private measures.

Introduces a new superregular random walk with controlled deviation.

Abstract

Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex - but very common - machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data for general compact metric spaces. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmicaly slowly.