Maintaining stream statistics over sliding windows: (extended abstract)
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining time-decaying stream aggregates
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Differential privacy under continual observation
Proceedings of the forty-second ACM symposium on Theory of computing
Differential privacy in new settings
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Private and continual release of statistics
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Calibrating noise to sensitivity in private data analysis
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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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.