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

Authors Clément L. Canonne , Yucheng Sun



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Clément L. Canonne
  • University of Sydney, School of Computer Science, Australia
Yucheng Sun
  • ETH Zürich, Switzerland

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Clément L. Canonne and Yucheng Sun. Private Distribution Testing with Heterogeneous Constraints: Your Epsilon Might Not Be Mine. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 23:1-23:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.23

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Security and privacy
Keywords
  • differential privacy
  • distribution testing
  • local privacy
  • shuffle privacy

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