Differential Privacy and the Fat-Shattering Dimension of Linear Queries

TL;DR

This paper explores how the accuracy of answering linear queries under differential privacy is fundamentally linked to the fat-shattering dimension, a measure of learnability for real-valued functions.

Contribution

It establishes a novel connection between differential privacy accuracy and the fat-shattering dimension of linear queries, broadening understanding of privacy-utility trade-offs.

Findings

Accuracy bounds are characterized by the fat-shattering dimension.

Linear queries' privacy-utility trade-offs depend on their learnability properties.

The work generalizes previous results to a wider class of queries.

Abstract

In this paper, we consider the task of answering linear queries under the constraint of differential privacy. This is a general and well-studied class of queries that captures other commonly studied classes, including predicate queries and histogram queries. We show that the accuracy to which a set of linear queries can be answered is closely related to its fat-shattering dimension, a property that characterizes the learnability of real-valued functions in the agnostic-learning setting.