A random polynomial-time algorithm for approximating the volume of convex bodies
Journal of the ACM (JACM)
Revealing information while preserving privacy
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Simulated annealing in convex bodies and an O*(n4) volume algorithm
Journal of Computer and System Sciences - Special issue on FOCS 2003
Smooth sensitivity and sampling in private data analysis
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The price of privacy and the limits of LP decoding
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Privacy, accuracy, and consistency too: a holistic solution to contingency table release
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The boundary between privacy and utility in data publishing
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
Mechanism Design via Differential Privacy
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A learning theory approach to non-interactive database privacy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
New Efficient Attacks on Statistical Disclosure Control Mechanisms
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Universally utility-maximizing privacy mechanisms
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the complexity of differentially private data release: efficient algorithms and hardness results
Proceedings of the forty-first annual ACM symposium on Theory of computing
Differentially private recommender systems: building privacy into the net
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
On the geometry of differential privacy
Proceedings of the forty-second ACM symposium on Theory of computing
Interactive privacy via the median mechanism
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the forty-second ACM symposium on Theory of computing
Optimizing linear counting queries under differential privacy
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Universally optimal privacy mechanisms for minimax agents
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Boosting and Differential Privacy
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Impossibility of Differentially Private Universally Optimal Mechanisms
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Optimal error of query sets under the differentially-private matrix mechanism
Proceedings of the 16th International Conference on Database Theory
The geometry of differential privacy: the sparse and approximate cases
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We investigate the problem of designing differentially private mechanisms for a set of d linear queries over a database, while adding as little error as possible. Hardt and Talwar [HT10] related this problem to geometric properties of a convex body defined by the set of queries and gave a O(log3 d)-approximation to the minimum l22 error, assuming a conjecture from convex geometry called the Slicing or Hyperplane conjecture. In this work we give a mechanism that works unconditionally, and also gives an improved O(log2 d) approximation to the expected l22 error. We remove the dependence on the Slicing conjecture by using a result of Klartag [Kla06] that shows that any convex body is close to one for which the conjecture holds; our main contribution is in making this result constructive by using recent techniques of Dadush, Peikert and Vempala [DPV10]. The improvement in approximation ratio relies on a stronger lower bound we derive on the optimum. This new lower bound goes beyond the packing argument that has traditionally been used in Differential Privacy and allows us to add the packing lower bounds obtained from orthogonal subspaces. We are able to achieve this via a symmetrization argument which argues that there always exists a near optimal differentially private mechanism which adds noise that is independent of the input database! We believe this result should be of independent interest, and also discuss some interesting consequences.