NDLI: Impossibility of Differentially Private Universally Optimal Mechanisms

Content Provider	IEEE Xplore Digital Library
Author	Brenner, H. Nissim, K.
Copyright Year	2010
Abstract	The notion of {\em a universally utility-maximizing privacy mechanism} was recently introduced by Ghosh, Rough garden, and Sundararajan~[STOC 2009]. These are mechanisms that guarantee optimal utility to a large class of information consumers, {\em simultaneously}, while preserving {\em Differential Privacy} [Dwork, McSherry, Nissim, and Smith, TCC 2006]. Ghosh, Rough garden and Sundararajan have demonstrated, quite surprisingly, a case where such a universally-optimal differentially-private mechanisms exists, when the information consumers are Bayesian. This result was recently extended by Gupte and Sundararajan~[PODS 2010] to risk-averse consumers. Both positive results deal with mechanisms (approximately) computing a {\em single count query} (i.e., the number of individuals satisfying a specific property in a given population), and the starting point of our work is a trial at extending these results to similar settings, such as sum queries with non-binary individual values, histograms, and two (or more) count queries. We show, however, that universally-optimal mechanisms do not exist for all these queries, both for Bayesian and risk-averse consumers. For the Bayesian case, we go further, and give a characterization of those functions that admit universally-optimal mechanisms, showing that a universally-optimal mechanism exists, essentially, only for a (single) count query. At the heart of our proof is a representation of a query function $f$ by its {\em privacy constraint graph} $G_f$ whose edges correspond to values resulting by applying $f$ to neighboring databases.
Starting Page	71
Ending Page	80
File Size	535855
Page Count	10
File Format	PDF
ISBN	9781424485253
ISSN	02725428
DOI	10.1109/FOCS.2010.13
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-10-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Privacy Databases Bayesian methods Data privacy Histograms Noise Degradation geometric mechanism differential privacy universally optimal mechanisms utility
Content Type	Text
Resource Type	Article

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