Representing Sparse Vectors with Differential Privacy, Low Error, Optimal Space, and Fast Access
Main Article Content
Representing a sparse histogram, or more generally a sparse vector, is a fundamental task in differential privacy.
An ideal solution would use 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 which show that the constant factors on the main performance parameters are quite small, suggesting practicality of the technique.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright is retained by the authors. By submitting to this journal, the author(s) license the article under the Creative Commons License – Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0), unless choosing a more lenient license (for instance, public domain). For situations not allowed under CC BY-NC-ND, short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source.
Authors of articles published by the journal grant the journal the right to store the articles in its databases for an unlimited period of time and to distribute and reproduce the articles electronically.