Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine

TL;DR

This paper explores private distribution testing when datasets have different privacy requirements, proposing algorithms that improve efficiency by considering heterogeneous privacy constraints in various differential privacy models.

Contribution

It formalizes the problem of distribution testing under heterogeneous privacy constraints and provides new algorithms tailored for local and shuffle privacy models.

Findings

Achieves better sample efficiency by accounting for different privacy levels.

Provides algorithms for local and shuffle privacy models.

Demonstrates advantages over traditional methods assuming equal privacy constraints.

Abstract

Private closeness testing asks to decide whether the underlying probability distributions of two sensitive datasets are identical or differ significantly in statistical distance, while guaranteeing (differential) privacy of the data. As in most (if not all) distribution testing questions studied under privacy constraints, however, previous work assumes that the two datasets are equally sensitive, i.e., must be provided the same privacy guarantees. This is often an unrealistic assumption, as different sources of data come with different privacy requirements; as a result, known closeness testing algorithms might be unnecessarily conservative, "paying" too high a privacy budget for half of the data. In this work, we initiate the study of the closeness testing problem under heterogeneous privacy constraints, where the two datasets come with distinct privacy requirements. We formalize the question and provide algorithms under the three most widely used differential privacy settings, with a particular focus on the local and shuffle models of privacy; and show that one can indeed achieve better sample efficiency when taking into account the two different "epsilon" requirements.