Iterative Constructions and Private Data Release
- Anupam GuptaAffiliated withComputer Science Department, Carnegie Mellon University
- , Aaron RothAffiliated withDepartment of Computer and Information Science, University of Pennsylvania
- , Jonathan UllmanAffiliated withSchool of Engineering and Applied Sciences, Harvard University
In this paper we study the problem of approximately releasing the cut function of a graph while preserving differential privacy, and give new algorithms (and new analyses of existing algorithms) in both the interactive and non-interactive settings.
Our algorithms in the interactive setting are achieved by revisiting the problem of releasing differentially private, approximate answers to a large number of queries on a database. We show that several algorithms for this problem fall into the same basic framework, and are based on the existence of objects which we call iterative database construction algorithms. We give a new generic framework in which new (efficient) IDC algorithms give rise to new (efficient) interactive private query release mechanisms. Our modular analysis simplifies and tightens the analysis of previous algorithms, leading to improved bounds. We then give a new IDC algorithm (and therefore a new private, interactive query release mechanism) based on the Frieze/Kannan low-rank matrix decomposition. This new release mechanism gives an improvement on prior work in a range of parameters where the size of the database is comparable to the size of the data universe (such as releasing all cut queries on dense graphs).
We also give a non-interactive algorithm for efficiently releasing private synthetic data for graph cuts with error O(|V|1.5). Our algorithm is based on randomized response and a non-private implementation of the SDP-based, constant-factor approximation algorithm for cut-norm due to Alon and Naor. Finally, we give a reduction based on the IDC framework showing that an efficient, private algorithm for computing sufficiently accurate rank-1 matrix approximations would lead to an improved efficient algorithm for releasing private synthetic data for graph cuts. We leave finding such an algorithm as our main open problem.
- Iterative Constructions and Private Data Release
- Book Title
- Theory of Cryptography
- Book Subtitle
- 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. Proceedings
- pp 339-356
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Ronald Cramer (16)
- Editor Affiliations
- 16. Cryptology Group, CWI Amsterdam; and Mathematical Institute, Leiden University, ,
- Author Affiliations
- 17. Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
- 18. Department of Computer and Information Science, University of Pennsylvania, Philadelphia, PA, USA, 19104
- 19. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, UK
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