On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Polynomial threshold functions, AC0 functions, and spectral norms
SIAM Journal on Computing
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
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
A learning theory approach to non-interactive database privacy
STOC '08 Proceedings of the fortieth 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
The Intersection of Two Halfspaces Has High Threshold Degree
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
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
PCPs and the hardness of generating private synthetic data
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Privately releasing conjunctions and the statistical query barrier
Proceedings of the forty-third annual ACM symposium on Theory of computing
On Arthur Merlin Games in Communication Complexity
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Private data release via learning thresholds
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Submodular functions are noise stable
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
The multiparty communication complexity of set disjointness
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
SIAM Journal on Computing
Faster algorithms for privately releasing marginals
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Low-weight halfspaces for sparse boolean vectors
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
The geometry of differential privacy: the sparse and approximate cases
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Answering n{2+o(1)} counting queries with differential privacy is hard
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Dual lower bounds for approximate degree and markov-bernstein inequalities
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We study the problem of answering k-way marginal queries on a database D ϵ ({0,1}d)n, while preserving differential privacy. The answer to a k-way marginal query is the fraction of the database's records x in {0,1}d with a given value in each of a given set of up to k columns. Marginal queries enable a rich class of statistical analyses on a dataset, and designing efficient algorithms for privately answering marginal queries has been identified as an important open problem in private data analysis. For any k, we give a differentially private online algorithm that runs in time poly (n, 2o(d)) per query and answers any sequence of poly(n) many k-way marginal queries with error at most ±0.01 on every query, provided n ≥ d0.51. To the best of our knowledge, this is the first algorithm capable of privately answering marginal queries with a non-trivial worst-case accuracy guarantee for databases containing poly(d, k) records in time exp(o(d)). Our algorithm runs the private multiplicative weights algorithm (Hardt and Rothblum, FOCS '10) on a new approximate polynomial representation of the database. We derive our representation for the database by approximating the OR function restricted to low Hamming weight inputs using low-degree polynomials with coefficients of bounded L1-norm. In doing so, we show new upper and lower bounds on the degree of such polynomials, which may be of independent approximation-theoretic interest.