TY - GEN
T1 - Private decayed predicate sums on streams
AU - Bolot, Jean
AU - Fawaz, Nadia
AU - Muthukrishnan, S.
AU - Nikolov, Aleksandar
AU - Taft, Nina
N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Continual privacy
KW - Decayed sums
KW - Differential privacy
KW - Online algorithms
UR - http://www.scopus.com/inward/record.url?scp=84875603068&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875603068&partnerID=8YFLogxK
U2 - 10.1145/2448496.2448530
DO - 10.1145/2448496.2448530
M3 - Conference contribution
AN - SCOPUS:84875603068
SN - 9781450315982
T3 - ACM International Conference Proceeding Series
SP - 284
EP - 295
BT - ICDT 2013 - 16th International Conference on Database Theory, Proceedings
T2 - 16th International Conference on Database Theory, ICDT 2013
Y2 - 18 March 2013 through 22 March 2013
ER -