Differential privacy in metric spaces: Numerical, categorical and functional data under the one roof

We study differential privacy in the abstract setting of probability on metric spaces. Numerical, categorical and functional data can be handled in a uniform manner in this setting. We demonstrate how mechanisms based on data sanitisation and those that rely on adding noise to query responses fit within this framework. We prove that once the sanitisation is differentially private, then so is the query response for any query. We show how to construct sanitisations for high-dimensional databases using simple 1-dimensional mechanisms. We also provide lower bounds on the expected error for differentially private sanitisations in the general metric space setting. Finally, we consider the question of sufficient sets for differential privacy and show that for relaxed differential privacy, any algebra generating the Borel ?-algebra is a sufficient set for relaxed differential privacy.

• Publication year

  2014

• Venue

  Information Sciences

• Publication date

  2014-02-25

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.ins.2015.01.021arXiv 1402.6124
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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