Unconditional differentially private mechanisms for linear queries

Bhaskara, Aditya; Dadush, Daniel; Krishnaswamy, Ravishankar; Talwar, Kunal

doi:10.1145/2213977.2214089

Cited by 48 publications

(65 citation statements)

References 30 publications

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“…Brenner and Nissim [9] showed that such universally optimal private mechanisms do not exist for two counting queries or for a single non-binary sum query. As mentioned above, Hardt and Talwar [32], and Bhaskara et al [5] gave relative guarantees for multi-dimensional queries under pure privacy with respect to total squared error. De [13] unified and strengthened these bounds and showed stronger lower bounds for the class of non-linear low sensitivity queries.…”

Section: Related Workmentioning

confidence: 95%

“…This is similar to the approach in [5,32] but we use the minimum volume enclosing ellipsoid, rather than the M -ellipsoid used in those works, to facilitate the decomposition process. This allows us to handle the approximate and the sparse cases.…”

Section: Theoremmentioning

confidence: 99%

“…Bhaskara et al [5] removed the dependence on the hyperplane conjecture and improved the approximation ratio to O(log 2 d). Can relaxing the privacy requirement to (ε, δ)-DP help with accuracy?…”

Section: Introductionmentioning

confidence: 99%

“…For a given set of d linear queries over a database x ∈ R N , we seek to find the differentially private mechanism that has the minimum mean squared error. For pure differential privacy, [5,32] give an O(log 2 d) approximation to the optimal mechanism. Our first contribution is to give an efficient O(log 2 d) approximation guarantee for the case of (ε, δ)-differential privacy.…”

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confidence: 99%

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The geometry of differential privacy

Nikolov

Talwar

Zhang

2013

Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing

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105

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We study trade-offs between accuracy and privacy in the context of linear queries over histograms. This is a rich class of queries that includes contingency tables and range queries and has been the focus of a long line of work. For a given set of d linear queries over a database x ∈ R N , we seek to find the differentially private mechanism that has the minimum mean squared error. For pure differential privacy, [5,32] give an O(log 2 d) approximation to the optimal mechanism. Our first contribution is to give an efficient O(log 2 d) approximation guarantee for the case of (ε, δ)-differential privacy. Our mechanism adds carefully chosen correlated Gaussian noise to the answers. We prove its approximation guarantee relative to the hereditary discrepancy lower bound of [44], using tools from convex geometry.We next consider the sparse case when the number of queries exceeds the number of individuals in the database, i.e. when d > nx 1. The lower bounds used in the previous approximation algorithm no longer apply -in fact better mechanisms are known in this setting [7,27,28,31,49]. Our second main contribution is to give an efficient (ε, δ)-differentially private mechanism that, for any given query set A and an upper bound n on x 1, has mean squared error within polylog(d, N ) of the optimal for A and n. This approximation is achieved by coupling the Gaussian noise addition approach with linear regression over the 1 ball. Additionally, we show a similar polylogarithmic approximation guarantee for the optimal ε-differentially private mechanism in this sparse setting. Our work also shows that for arbitrary counting queries, i.e. A with entries in {0, 1}, there is an ε-differentially private mechanism with expected errorÕ( √ n) per query, improving on theÕ(n 2 3 ) bound of [7] and matching the lower bound implied by [15] up to logarithmic factors.The connection between the hereditary discrepancy and the privacy mechanism enables us to derive the first polylogarithmic approximation to the hereditary discrepancy of a matrix A.

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Section: Related Workmentioning

confidence: 95%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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The geometry of differential privacy

Nikolov

Talwar

Zhang

2013

Proceedings of the Forty-Fifth Annual ACM Symposium on Theory of Computing

Self Cite

105

View full text Add to dashboard Cite

show abstract

“…Other approaches [41,42] used convex geometry to devise differentially private mechanisms and upper/lower bounds for query workloads. These schemes were based on the exponential mechanism.…”

Section: ) Linear Counting Queriesmentioning

confidence: 99%

Differential Privacy in Practice

Nguyen

Kim

2013

Journal of Computing Science and Engineering

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We briefly review the problem of statistical disclosure control under differential privacy model, which entails a formal and ad omnia privacy guarantee separating the utility of the database and the risk due to individual participation. It has born fruitful results over the past ten years, both in theoretical connections to other fields and in practical applications to real-life datasets. Promises of differential privacy help to relieve concerns of privacy loss, which hinder the release of community-valuable data. This paper covers main ideas behind differential privacy, its interactive versus non-interactive settings, perturbation mechanisms, and typical applications found in recent research. Category: Smart and intelligent computing

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Geometric Approaches to Answering Queries

Nikolov

2016

Encyclopedia of Algorithms

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Unconditional differentially private mechanisms for linear queries

Cited by 48 publications

References 30 publications

The geometry of differential privacy

The geometry of differential privacy

Differential Privacy in Practice

Geometric Approaches to Answering Queries

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