research-article

Optimizing linear counting queries under differential privacy

Authors:

Vibhor Rastogi,

Andrew McGregorAuthors Info & Claims

PODS '10: Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems

Pages 123 - 134

https://doi.org/10.1145/1807085.1807104

Published: 06 June 2010 Publication 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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Cited By

Cao ZWu SLi XZhang H(2025)Differentially private histogram with valid statisticsStatistics & Probability Letters10.1016/j.spl.2024.110354219(110354)Online publication date: Apr-2025
https://doi.org/10.1016/j.spl.2024.110354
Chen JZhou SQiu JXu YZeng BFang WChen XHuang YXu ZChen Y(2024)A Histogram Publishing Method under Differential Privacy That Involves Balancing Small-Bin Availability FirstAlgorithms10.3390/a1707029317:7(293)Online publication date: 4-Jul-2024
https://doi.org/10.3390/a17070293
Poepsel-Lemaitre RBeedkar KMarkl V(2024)Disclosure-Compliant Query AnsweringProceedings of the ACM on Management of Data10.1145/36988082:6(1-28)Online publication date: 20-Dec-2024
https://dl.acm.org/doi/10.1145/3698808
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Optimizing linear counting queries under differential privacy

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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

General Chair:
Jan Paredaens
University of Antwerp, Belgium
,
Program Chair:
Dirk Van Gucht
Indiana University, USA

Copyright © 2010 ACM.

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New York, NY, United States

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Published: 06 June 2010

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SIGMOD/PODS '10: International Conference on Management of Data

June 6 - 11, 2010

Indiana, Indianapolis, USA

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PODS '10 Paper Acceptance Rate 27 of 113 submissions, 24%;

Overall Acceptance Rate 642 of 2,707 submissions, 24%

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Cited By

Cao ZWu SLi XZhang H(2025)Differentially private histogram with valid statisticsStatistics & Probability Letters10.1016/j.spl.2024.110354219(110354)Online publication date: Apr-2025
https://doi.org/10.1016/j.spl.2024.110354
Chen JZhou SQiu JXu YZeng BFang WChen XHuang YXu ZChen Y(2024)A Histogram Publishing Method under Differential Privacy That Involves Balancing Small-Bin Availability FirstAlgorithms10.3390/a1707029317:7(293)Online publication date: 4-Jul-2024
https://doi.org/10.3390/a17070293
Poepsel-Lemaitre RBeedkar KMarkl V(2024)Disclosure-Compliant Query AnsweringProceedings of the ACM on Management of Data10.1145/36988082:6(1-28)Online publication date: 20-Dec-2024
https://dl.acm.org/doi/10.1145/3698808
Cai JYe QHu HLiu XFu Y(2024)Boosting Accuracy of Differentially Private Continuous Data Release for Federated LearningIEEE Transactions on Information Forensics and Security10.1109/TIFS.2024.347732519(10287-10301)Online publication date: 2024
https://doi.org/10.1109/TIFS.2024.3477325
Cai JLiu XYe QLiu YWang Y(2024)A Federated Learning Framework Based on Differentially Private Continuous Data ReleaseIEEE Transactions on Dependable and Secure Computing10.1109/TDSC.2024.3364060(1-16)Online publication date: 2024
https://doi.org/10.1109/TDSC.2024.3364060
Cai JLiu XLi JChoo K(2024)Differentially Private Non-Negative Consistent Release for Large-Scale Hierarchical TreesIEEE Transactions on Dependable and Secure Computing10.1109/TDSC.2023.325352021:1(388-402)Online publication date: Jan-2024
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Jiang BDu JSharma SYan Q(2024)Budget Recycling Differential Privacy2024 IEEE Symposium on Security and Privacy (SP)10.1109/SP54263.2024.00212(1028-1046)Online publication date: 19-May-2024
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Bojkovic NLoh P(2024)Differentially Private Synthetic Data with Private Density Estimation2024 IEEE International Symposium on Information Theory (ISIT)10.1109/ISIT57864.2024.10619641(599-604)Online publication date: 7-Jul-2024
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Baek IChung Y(2024)Differentially private and explainable boosting machine with enhanced utilityNeurocomputing10.1016/j.neucom.2024.128424(128424)Online publication date: Aug-2024
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Fu CLi HLou JCui J(2024)Towards answering analytical query over hierarchical histogram under untrusted serversDistributed and Parallel Databases10.1007/s10619-024-07447-343:1Online publication date: 12-Nov-2024
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