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Optimizing linear counting queries under differential privacy

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Published:06 June 2010Publication History

ABSTRACT

Differential privacy is a robust privacy standard that has been successfully applied to a range of data analysis tasks. But despite much recent work, optimal strategies for answering a collection of related queries are not known.

We propose the matrix mechanism, a new algorithm for answering a workload of predicate counting queries. Given a workload, the mechanism requests answers to a different set of queries, called a query strategy, which are answered using the standard Laplace mechanism. Noisy answers to the workload queries are then derived from the noisy answers to the strategy queries. This two stage process can result in a more complex correlated noise distribution that preserves differential privacy but increases accuracy.

We provide a formal analysis of the error of query answers produced by the mechanism and investigate the problem of computing the optimal query strategy in support of a given workload. We show this problem can be formulated as a rank-constrained semidefinite program. Finally, we analyze two seemingly distinct techniques, whose similar behavior is explained by viewing them as instances of the matrix mechanism.

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          • Published in

            cover image ACM Conferences
            PODS '10: Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
            June 2010
            350 pages
            ISBN:9781450300339
            DOI:10.1145/1807085

            Copyright © 2010 ACM

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            Association for Computing Machinery

            New York, NY, United States

            Publication History

            • Published: 6 June 2010

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