Differentially Private Medians and Interior Points for Non-Pathological Data

Authors Maryam Aliakbarpour, Rose Silver, Thomas Steinke, Jonathan Ullman



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Author Details

Maryam Aliakbarpour
  • Department of Computer Science, Rice University, Houston, TX, USA
Rose Silver
  • Khoury College of Computer Sciences, Northeastern University, Boston, MA, USA
Thomas Steinke
  • Google DeepMind, Mountain View, CA, USA
Jonathan Ullman
  • Khoury College of Computer Sciences, Northeastern University, Boston, MA, USA

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Maryam Aliakbarpour, Rose Silver, Thomas Steinke, and Jonathan Ullman. Differentially Private Medians and Interior Points for Non-Pathological Data. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.3

Abstract

We construct sample-efficient differentially private estimators for the approximate-median and interior-point problems, that can be applied to arbitrary input distributions over ℝ satisfying very mild statistical assumptions. Our results stand in contrast to the surprising negative result of Bun et al. (FOCS 2015), which showed that private estimators with finite sample complexity cannot produce interior points on arbitrary distributions.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory of database privacy and security
Keywords
  • Differential Privacy
  • Statistical Estimation
  • Approximate Medians
  • Interior Point Problem

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References

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