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A learning theory approach to non-interactive database privacy (2008)
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| Venue: | In Proceedings of the 40th annual ACM symposium on Theory of computing |
| Citations: | 218 - 25 self |
BibTeX
@INPROCEEDINGS{Blum08alearning,
author = {Avrim Blum and Katrina Ligett},
title = {A learning theory approach to non-interactive database privacy},
booktitle = {In Proceedings of the 40th annual ACM symposium on Theory of computing},
year = {2008},
pages = {609--618},
publisher = {ACM}
}
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Abstract
In this paper we demonstrate that, ignoring computational constraints, it is possible to release synthetic databases that are useful for accurately answering large classes of queries while preserving differential privacy. Specifically, we give a mechanism that privately releases synthetic data useful for answering a class of queries over a discrete domain with error that grows as a function of the size of the smallest net approximately representing the answers to that class of queries. We show that this in particular implies a mechanism for counting queries that gives error guarantees that grow only with the VC-dimension of the class of queries, which itself grows at most logarithmically with the size of the query class. We also show that it is not possible to release even simple classes of queries (such as intervals and their generalizations) over continuous domains with worst-case utility guarantees while preserving differential privacy. In response to this, we consider a relaxation of the utility guarantee and give a privacy preserving polynomial time algorithm that for any halfspace query will provide an answer that is accurate for some small perturbation of the query. This algorithm does not release synthetic data, but instead another data structure capable of representing an answer for each query. We also give an efficient algorithm for releasing synthetic data for the class of interval queries and axis-aligned rectangles of constant dimension over discrete domains. 1.
Keyphrases
learning theory approach non-interactive database privacy synthetic data discrete domain differential privacy polynomial time algorithm simple class error guarantee large class axis-aligned rectangle halfspace query small perturbation data structure continuous domain query class interval query computational constraint synthetic database constant dimension worst-case utility guarantee particular implies utility guarantee efficient algorithm
