Private decayed predicate sums on streams

Jean Bolot, Nadia Fawaz, S. Muthukrishnan, Aleksandar Nikolov, Nina Taft

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In many monitoring applications, recent data is more important than distant data. How does this affect privacy of data analysis? We study a general class of data analyses - predicate sums - in this context. Formally, we study the problem of estimating predicate sums privately, for sliding windows and other decay models. While we require accuracy in analysis with respect to the decayed sums, we still want differential privacy for the entire past. This is challenging because window sums are not monotonic or even near-monotonic as the problems studied previously [DPNR10]. We present accurate ε-differentially private algorithms for decayed sums. For window and exponential decay sums, our algorithms are accurate up to additive 1/ε and polylog terms in the range of the computed function; for polynomial decay sums which are technically more challenging because partial solutions do not compose easily, our algorithms incur additional relative error. Our algorithm for polynomial decay sums generalizes to arbitrary decay sum functions. The algorithm crucially relies on our solution for the window sum problem as a subroutine. Further, we show lower bounds, tight within polylog factors and tight with respect to the dependence on the probability of error. Our results are obtained via a natural dyadic tree we maintain, but the crux is we treat the tree data structure in non-uniform manner. We also extend our study and consider the "dual" question of maintaining conventional running sums on the entire data thus far, but when privacy constraints expire with time. We define a new model of privacy with expiration and consider the problems of designing accurate running sum and linear map algorithms in this model. Now the goal is to design algorithms whose accuracy guarantees scale with the size of the privacy window. We reduce running sum with a privacy window W to window sum without privacy expiration,and characterize the accuracy of output perturbation for general linear maps with privacy window W.

Original languageEnglish (US)
Title of host publicationICDT 2013 - 16th International Conference on Database Theory, Proceedings
Pages284-295
Number of pages12
DOIs
StatePublished - Apr 4 2013
Externally publishedYes
Event16th International Conference on Database Theory, ICDT 2013 - Genoa, Italy
Duration: Mar 18 2013Mar 22 2013

Publication series

NameACM International Conference Proceeding Series

Conference

Conference16th International Conference on Database Theory, ICDT 2013
CountryItaly
CityGenoa
Period3/18/133/22/13

Keywords

  • Continual privacy
  • Decayed sums
  • Differential privacy
  • Online algorithms

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications

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  • Cite this

    Bolot, J., Fawaz, N., Muthukrishnan, S., Nikolov, A., & Taft, N. (2013). Private decayed predicate sums on streams. In ICDT 2013 - 16th International Conference on Database Theory, Proceedings (pp. 284-295). (ACM International Conference Proceeding Series). https://doi.org/10.1145/2448496.2448530