Exploiting Metric Structure for Efficient Private Query Release

@article{Huang2012ExploitingMS,
  title={Exploiting Metric Structure for Efficient Private Query Release},
  author={Zhiyi Huang and Aaron Roth},
  journal={ArXiv},
  year={2012},
  volume={abs/1211.7302}
}
We consider the problem of privately answering queries defined on databases which are collections of points belonging to some metric space. We give simple, computationally efficient algorithms for answering distance queries defined over an arbitrary metric. Distance queries are specified by points in the metric space, and ask for the average distance from the query point to the points contained in the database, according to the specified metric. Our algorithms run efficiently in the database… 

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References

SHOWING 1-10 OF 23 REFERENCES

Fast Private Data Release Algorithms for Sparse Queries

This paper considers the large class of sparse queries, which take non-zero values on only polynomially many universe elements, and gives efficient query release algorithms for this class, in both the interactive and the non-interactive setting.

Answering n{2+o(1)} counting queries with differential privacy is hard

It is proved that if one-way functions exist, then there is no algorithm that takes as input a database db ∈ dbset, and k = ~Ω(n2) arbitrary efficiently computable counting queries, runs in time poly(d, n), and returns an approximate answer to each query, while satisfying differential privacy.

Privately releasing conjunctions and the statistical query barrier

The number of statistical queries necessary and sufficient for this task is equal to the agnostic learning complexity of C in Kearns' statistical query (SQ)model, which isolates the complexity of agnosticLearning in the SQ-model as a new barrier in the design of differentially private algorithms.

Interactive privacy via the median mechanism

The median mechanism is the first privacy mechanism capable of identifying and exploiting correlations among queries in an interactive setting, and an efficient implementation is given, with running time polynomial in the number of queries, the database size, and the domain size.

Iterative Constructions and Private Data Release

New algorithms (and new analyses of existing algorithms) in both the interactive and non-interactive settings are given, and a reduction based on the IDC framework shows 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.

Faster Algorithms for Privately Releasing Marginals

To the knowledge, this work is the first algorithm capable of privately releasing marginal queries with non-trivial worst-case accuracy guarantees in time substantially smaller than the number of k-way marginal queries, which is dΘ(k) (for k≪d).

Mirror Descent Based Database Privacy

This paper forms a generic IDC framework based on the Mirror Descent algorithm, a popular convex optimization algorithm, and presents two concrete applications, namely, cut queries over a bipartite graph and linear queries over low-rank matrices, and provides significantly tighter error bounds.

A Multiplicative Weights Mechanism for Privacy-Preserving Data Analysis

A new differentially private multiplicative weights mechanism for answering a large number of interactive counting (or linear) queries that arrive online and may be adaptively chosen, and it is shown that when the input database is drawn from a smooth distribution — a distribution that does not place too much weight on any single data item — accuracy remains as above, and the running time becomes poly-logarithmic in the data universe size.

On the complexity of differentially private data release: efficient algorithms and hardness results

Private data analysis in the setting in which a trusted and trustworthy curator releases to the public a "sanitization" of the data set that simultaneously protects the privacy of the individual contributors of data and offers utility to the data analyst is considered.

Practical privacy: the SuLQ framework

This work considers a statistical database in which a trusted administrator introduces noise to the query responses with the goal of maintaining privacy of individual database entries, and modify the privacy analysis to real-valued functions f and arbitrary row types, greatly improving the bounds on noise required for privacy.