Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling

Authors Mark Bun, Jörg Drechsler, Marco Gaboardi, Audra McMillan, Jayshree Sarathy

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Mark Bun
  • Department of Computer Science, Boston University, MA, USA
Jörg Drechsler
  • Institute for Employment Research, Nürnberg, Germany
  • Joint Program in Survey Methodology, University of Maryland, College Park, MD, USA
Marco Gaboardi
  • Department of Computer Science, Boston University, MA, USA
Audra McMillan
  • Apple, Cupertino, CA, USA
Jayshree Sarathy
  • Harvard John A. Paulson School of Engineering and Applied Sciences, Boston, MA, USA

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Mark Bun, Jörg Drechsler, Marco Gaboardi, Audra McMillan, and Jayshree Sarathy. Controlling Privacy Loss in Sampling Schemes: An Analysis of Stratified and Cluster Sampling. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Sampling schemes are fundamental tools in statistics, survey design, and algorithm design. A fundamental result in differential privacy is that a differentially private mechanism run on a simple random sample of a population provides stronger privacy guarantees than the same algorithm run on the entire population. However, in practice, sampling designs are often more complex than the simple, data-independent sampling schemes that are addressed in prior work. In this work, we extend the study of privacy amplification results to more complex, data-dependent sampling schemes. We find that not only do these sampling schemes often fail to amplify privacy, they can actually result in privacy degradation. We analyze the privacy implications of the pervasive cluster sampling and stratified sampling paradigms, as well as provide some insight into the study of more general sampling designs.

Subject Classification

ACM Subject Classification
  • Security and privacy → Privacy protections
  • privacy
  • differential privacy
  • survey design
  • survey sampling


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