Differential Privacy and the Fat-Shattering Dimension of Linear 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.