### 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 language | English (US) |
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Title of host publication | ICDT 2013 - 16th International Conference on Database Theory, Proceedings |

Pages | 284-295 |

Number of pages | 12 |

DOIs | |

State | Published - Apr 4 2013 |

Event | 16th International Conference on Database Theory, ICDT 2013 - Genoa, Italy Duration: Mar 18 2013 → Mar 22 2013 |

### Publication series

Name | ACM International Conference Proceeding Series |
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### Conference

Conference | 16th International Conference on Database Theory, ICDT 2013 |
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Country | Italy |

City | Genoa |

Period | 3/18/13 → 3/22/13 |

### Fingerprint

### Keywords

- Continual privacy
- Decayed sums
- Differential privacy
- Online algorithms

### ASJC Scopus subject areas

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

### Cite this

*ICDT 2013 - 16th International Conference on Database Theory, Proceedings*(pp. 284-295). (ACM International Conference Proceeding Series). https://doi.org/10.1145/2448496.2448530

**Private decayed predicate sums on streams.** / Bolot, Jean; Fawaz, Nadia; Muthukrishnan, Shanmugavelayutham; Nikolov, Aleksandar; Taft, Nina.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ICDT 2013 - 16th International Conference on Database Theory, Proceedings.*ACM International Conference Proceeding Series, pp. 284-295, 16th International Conference on Database Theory, ICDT 2013, Genoa, Italy, 3/18/13. https://doi.org/10.1145/2448496.2448530

}

TY - GEN

T1 - Private decayed predicate sums on streams

AU - Bolot, Jean

AU - Fawaz, Nadia

AU - Muthukrishnan, Shanmugavelayutham

AU - Nikolov, Aleksandar

AU - Taft, Nina

PY - 2013/4/4

Y1 - 2013/4/4

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

ER -