The Laplace Mechanism has optimal utility for differential privacy over continuous queries

Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also decreases its utility. Yet it has been shown tha...

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Published in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 12
Main Authors: Fernandes, Natasha, McIver, Annabelle, Morgan, Carroll
Format: Conference Proceeding
Language:English
Published: IEEE 29.06.2021
Subjects:
abstract channels
Computer science
Differential privacy
hyper-distributions
Laplace mechanism
optimal mechanisms
quantitative information flow
utility
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Abstract Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also decreases its utility. Yet it has been shown that for discrete data (e.g. counting queries), a mandated degree of privacy and a reasonable interpretation of loss of utility, the Geometric obfuscating mechanism is optimal: it loses as little utility as possible [Ghosh et al. [1]].For continuous query results however (e.g. real numbers) the optimality result does not hold. Our contribution here is to show that optimality is regained by using the Laplace mechanism for the obfuscation.The technical apparatus involved includes the earlier discrete result [Ghosh op. cit.], recent work on abstract channels and their geometric representation as hyper-distributions [Alvim et al. [2]], and the dual interpretations of distance between distributions provided by the Kantorovich-Rubinstein Theorem.
AbstractList Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the query results makes the released information less specific but, unavoidably, also decreases its utility. Yet it has been shown that for discrete data (e.g. counting queries), a mandated degree of privacy and a reasonable interpretation of loss of utility, the Geometric obfuscating mechanism is optimal: it loses as little utility as possible [Ghosh et al. [1]].For continuous query results however (e.g. real numbers) the optimality result does not hold. Our contribution here is to show that optimality is regained by using the Laplace mechanism for the obfuscation.The technical apparatus involved includes the earlier discrete result [Ghosh op. cit.], recent work on abstract channels and their geometric representation as hyper-distributions [Alvim et al. [2]], and the dual interpretations of distance between distributions provided by the Kantorovich-Rubinstein Theorem.
Author McIver, Annabelle
Fernandes, Natasha
Morgan, Carroll
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  organization: UNSW,School of Computer Science and Engineering,Sydney
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Snippet Differential Privacy protects individuals' data when statistical queries are published from aggregated databases: applying "obfuscating" mechanisms to the...
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SubjectTerms abstract channels
Computer science
Differential privacy
hyper-distributions
Laplace mechanism
optimal mechanisms
quantitative information flow
utility
Title The Laplace Mechanism has optimal utility for differential privacy over continuous queries
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