The weighted majority algorithm
Information and Computation
Weakly learning DNF and characterizing statistical query learning using Fourier analysis
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Efficient noise-tolerant learning from statistical queries
Journal of the ACM (JACM)
A sharp concentration inequality with application
Random Structures & Algorithms
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
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating submodular functions everywhere
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Concentration of Measure for the Analysis of Randomized Algorithms
Concentration of Measure for the Analysis of Randomized Algorithms
Near-optimal observation selection using submodular functions
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
A Practical Differentially Private Random Decision Tree Classifier
ICDMW '09 Proceedings of the 2009 IEEE International Conference on Data Mining Workshops
A Complete Characterization of Statistical Query Learning with Applications to Evolvability
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis
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
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
Optimal private halfspace counting via discrepancy
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Iterative constructions and private data release
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Distributed private heavy hitters
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Faster algorithms for privately releasing marginals
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A learning theory approach to noninteractive database privacy
Journal of the ACM (JACM)
Differential privacy for the analyst via private equilibrium computation
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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
Faster private release of marginals on small databases
Proceedings of the 5th conference on Innovations in theoretical computer science
Mechanism design in large games: incentives and privacy
Proceedings of the 5th conference on Innovations in theoretical computer science
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Suppose we would like to know all answers to a set of statistical queries C on a data set up to small error, but we can only access the data itself using statistical queries. A trivial solution is to exhaustively ask all queries in C. Can we do any better? We show that the number of statistical queries necessary and sufficient for this task is---up to polynomial factors---equal to the agnostic learning complexity of C in Kearns' statistical query (SQ)model. This gives a complete answer to the question when running time is not a concern. We then show that the problem can be solved efficiently (allowing arbitrary error on a small fraction of queries) whenever the answers to C can be described by a submodular function. This includes many natural concept classes, such as graph cuts and Boolean disjunctions and conjunctions. While interesting from a learning theoretic point of view, our main applications are in privacy-preserving data analysis: Here, our second result leads to an algorithm that efficiently releases differentially private answers to all Boolean conjunctions with 1% average error. This presents progress on a key open problem in privacy-preserving data analysis. Our first result on the other hand gives unconditional lower bounds on any differentially private algorithm that admits a (potentially non-privacy-preserving) implementation using only statistical queries. Not only our algorithms, but also most known private algorithms can be implemented using only statistical queries, and hence are constrained by these lower bounds. Our result therefore isolates the complexity of agnostic learning in the SQ-model as a new barrier in the design of differentially private algorithms.