Representing Sparse Vectors with Differential Privacy, Low Error, Optimal Space, and Fast Access

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt


Representing a sparse histogram, or more generally a sparse vector, is a fundamental task in differential privacy. An ideal solution would require space close to information-theoretical lower bounds, have an error distribution that depends optimally on the desired privacy level, and allow fast random access to entries in the vector. However, existing approaches have only achieved two of these three goals. In this paper we introduce the Approximate Laplace Projection (ALP) mechanism for approximating k-sparse vectors. This mechanism is shown to simultaneously have information-theoretically optimal space (up to constant factors), fast access to vector entries, and error of the same magnitude as the Laplace mechanism applied to dense vectors. A key new technique is a unary representation of small integers, which we show to be robust against “randomized response” noise. This representation is combined with hashing, in the spirit of Bloom filters, to obtain a space-efficient, differentially private representation. Our theoretical performance bounds are complemented by simulations showing that the constant factors on the main performance parameters are quite small and supporting practicality of the technique.

TidsskriftJournal of Privacy and Confidentiality
Udgave nummer2
Antal sider35
StatusUdgivet - 2022

Bibliografisk note

Funding Information:
Acknowledgments. We thank the anonymous reviewers of the TPDP’21 workshop, and the ACM CCS conference, and the Journal of Privacy and Confidentiality for their detailed suggestions that helped improve the paper. We thank Jakub Tˇetek for discussions that led to the results mentioned in Section 6. Christian Janos Lebeda and Rasmus Pagh are affiliated with Basic Algorithms Research Copenhagen (BARC), supported by the VILLUM Foundation grant 16582.

Publisher Copyright:
© 2022, Cornell University. All rights reserved.

ID: 340691561