Discrepancy of set-systems and matrices
European Journal of Combinatorics
Handbook of combinatorics (vol. 2)
The discrepancy method: randomness and complexity
The discrepancy method: randomness and complexity
Revealing information while preserving privacy
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Practical privacy: the SuLQ framework
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
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
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
Private and continual release of statistics
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Differentially private data release through multidimensional partitioning
SDM'10 Proceedings of the 7th VLDB conference on Secure data management
Constructive Algorithms for Discrepancy Minimization
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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
Boosting the accuracy of differentially private histograms through consistency
Proceedings of the VLDB Endowment
Differentially private data cubes: optimizing noise sources and consistency
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Privately releasing conjunctions and the statistical query barrier
Proceedings of the forty-third annual ACM symposium on Theory of computing
On Range Searching in the Group Model and Combinatorial Discrepancy
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
An adaptive mechanism for accurate query answering under differential privacy
Proceedings of the VLDB Endowment
Our data, ourselves: privacy via distributed noise generation
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Unconditional differentially private mechanisms for linear queries
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Optimal private halfspace counting via discrepancy
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Lower bounds in differential privacy
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Iterative constructions and private data release
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Minimax Rates of Estimation for High-Dimensional Linear Regression Over $\ell_q$ -Balls
IEEE Transactions on Information Theory
Low-rank mechanism: optimizing batch queries under differential privacy
Proceedings of the VLDB Endowment
Probabilistic Relational Reasoning for Differential Privacy
ACM Transactions on Programming Languages and Systems (TOPLAS)
Faster private release of marginals on small databases
Proceedings of the 5th conference on Innovations in theoretical computer science
Integer feasibility of random polytopes: random integer programs
Proceedings of the 5th conference on Innovations in theoretical computer science
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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 ∈ RN, we seek to find the differentially private mechanism that has the minimum mean squared error. For pure differential privacy, [5, 32] give an O(log2 d) approximation to the optimal mechanism. Our first contribution is to give an efficient O(log2 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 n Δ |x|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 l1 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 error ~O(√n) per query, improving on the ~O(n2/3) 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.