On the fine asymptotics of information theoretic privacy

Kousha Kalantari, Oliver Kosut, Lalitha Sankar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

The tradeoff between privacy and utility is studied for small datasets using tools from fixed error asymptotics in information theory. The problem is formulated as determining the privacy mechanism (random mapping) which minimizes the mutual information (a metric for privacy leakage) between the private features of the original dataset and a released version, subject to a distortion constraint between the public features and the released version. An excess probability bound is used to constrain the distortion, thus limiting the random variation in distortion due to the finite length. Bounds are derived for the following variants of the problem: (1) whether the mechanism is memoryless (local privacy) or not (global privacy), (2) whether the privacy mechanism has direct access to the private data or not. It is shown that these settings yield different performance in the first order: for global privacy, the first-order leakage decreases with the excess probability, whereas for local privacy it remains constant. The derived bounds also provide tight performance results up to second order for local privacy, as well as bounds on the second order term for global privacy.

Original languageEnglish (US)
Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages532-539
Number of pages8
ISBN (Electronic)9781509045495
DOIs
StatePublished - Feb 10 2017
Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
Duration: Sep 27 2016Sep 30 2016

Other

Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
CountryUnited States
CityMonticello
Period9/27/169/30/16

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Keywords

  • excess distortion
  • fine asymptotics
  • mutual information leakage
  • Privacy utility trade off

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Control and Optimization

Cite this

Kalantari, K., Kosut, O., & Sankar, L. (2017). On the fine asymptotics of information theoretic privacy. In 54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 (pp. 532-539). [7852277] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ALLERTON.2016.7852277