## An Adaptive Mechanism for Accurate Query Answering under Differential Privacy

Citations: | 8 - 2 self |

### BibTeX

@MISC{Li_anadaptive,

author = {Chao Li and Gerome Miklau},

title = {An Adaptive Mechanism for Accurate Query Answering under Differential Privacy},

year = {}

}

### OpenURL

### Abstract

We propose a novel mechanism for answering sets of counting queries under differential privacy. Given a workload of counting queries, the mechanism automatically selects a different set of “strategy ” queries to answer privately, using those answers to derive answers to the workload. The main algorithm proposed in this paper approximates the optimal strategy for any workload of linear counting queries. With no cost to the privacy guarantee, the mechanism improves significantly on prior approaches and achieves near-optimal error for many workloads, when applied under (ɛ, δ)-differential privacy. The result is an adaptive mechanism which can help users achieve good utility without requiring that they reason carefully about the best formulation of their task. 1.

### Citations

3669 | Convex Optimization - BOYD, VANDENBERGHE - 2004 |

313 | Calibrating noise to sensitivity in private data analysis
- Dwork, McSherry, et al.
- 2006
(Show Context)
Citation Context ...e result is an adaptive mechanism which can help users achieve good utility without requiring that they reason carefully about the best formulation of their task. 1. INTRODUCTION Differential privacy =-=[10]-=- guarantees that information released about participants in a data set will be virtually indistinguishable whether or not their personal data is included. There are now many algorithms satisfying diff... |

90 | Our data, ourselves: privacy via distributed noise generation
- Dwork, Kenthapadi, et al.
- 2006
(Show Context)
Citation Context ...escribed in (c). answers for any two neighboring databases. For database instance I, we denote by nbrs(I) the set of databases differing from I in at most one record. Approximate differential privacy =-=[9, 17]-=-, is a modest relaxation in which the ɛ bound on query answer probabilities may be violated with small probability (controlled by δ). Definition 4. (Approximate Differential Privacy) A randomized algo... |

71 | Differentially Private Recommender Systems : Building Privacy into the Netflix Prize Contenders
- McSherry, Mironov
- 2009
(Show Context)
Citation Context ...escribed in (c). answers for any two neighboring databases. For database instance I, we denote by nbrs(I) the set of databases differing from I in at most one record. Approximate differential privacy =-=[9, 17]-=-, is a modest relaxation in which the ɛ bound on query answer probabilities may be violated with small probability (controlled by δ). Definition 4. (Approximate Differential Privacy) A randomized algo... |

67 |
Privacy integrated queries: an extensible platform for privacy-preserving data analysis
- McSherry
- 2009
(Show Context)
Citation Context ... about alternative mechanisms and the formulation of their task. Their choices may have a significant impact on the utility of the output, for the same level of privacy. Even using the PINQ framework =-=[16]-=-, designed to aid uninitiated users in writing differentially-private programs, users can be faced with vastly different degrees of accuracy depending on how their task is expressed. Further, there ar... |

59 | A firm foundation for private data analysis - Dwork - 2011 |

52 | Universally utility-maximizing privacy mechanisms
- Ghosh, Roughgarden, et al.
- 2009
(Show Context)
Citation Context ...if better utility is possible with a 1 For a single numerical query, the addition of appropriatelyscaled discrete Laplace noise satisfies ɛ-differential privacy and has been proven optimally accurate =-=[11]-=-. For workloads of multiple queries, optimally accurate mechanisms are not known. different algorithm, or if their utility goals are fundamentally incompatible with differential privacy. In this work,... |

44 | Differential privacy via wavelet transforms
- Xiao, Wang, et al.
- 2010
(Show Context)
Citation Context ...es using the Laplace mechanism, and then derive the desired marginals [4]. For workloads consisting of all range-count queries over an or-dered domain, two approaches have been proposed. Xiao et al. =-=[21]-=- first answer a set of wavelet basis queries, while Hay et al. [13] use a hierarchical set of counting queries which recursively decompose the domain. For workloads consisting of sets of marginals, Di... |

41 | Optimizing linear counting queries under differential privacy
- Li, Hay, et al.
- 2010
(Show Context)
Citation Context ... but with an alternative basis.6. RELATED WORK The present work uses the framework of the matrix mechanism to develop an adaptive query answering algorithm. The original work on the matrix mechanism =-=[14]-=- described and analyzed in a unified framework two prior techniques specifically tailored to range queries. The first used a wavelet transformation [21]; the second used a hierarchical set of queries ... |

31 |
Boosting the accuracy of differentially private histograms through consistency
- Hay, Rastogi, et al.
- 2010
(Show Context)
Citation Context ... [4]. For workloads consisting of all range-count queries over an or514dered domain, two approaches have been proposed. Xiao et al. [21] first answer a set of wavelet basis queries, while Hay et al. =-=[13]-=- use a hierarchical set of counting queries which recursively decompose the domain. For workloads consisting of sets of marginals, Ding et al. [7] recently proposed a method for selecting an alternati... |

26 | Boosting the accuracy of differentially-private histograms through consistency
- Hay, Rastogi, et al.
- 2010
(Show Context)
Citation Context ...ls [4]. For workloads consisting of all range-count queries over an or-dered domain, two approaches have been proposed. Xiao et al. [21] first answer a set of wavelet basis queries, while Hay et al. =-=[13]-=- use a hierarchical set of counting queries which recursively decompose the domain. For workloads consisting of sets of marginals, Ding et al. [7] recently proposed a method for selecting an alternati... |

22 | Interactive privacy via the median mechanism
- Roth, Roughgarden
- 2010
(Show Context)
Citation Context ...datadependent algorithm to minimize the relative error with an innovative resampling function. Data-dependent interactive (as opposed to batch) mechanisms have been considered by Roth and Roughgarden =-=[19]-=-, who answer predicate queries on databases with 0-1 entries. Hardt et. al [12] provide a linear time algorithm for the same query and database setting. 7. CONCLUSIONS AND FUTURE WORK We have describe... |

19 | A multiplicative weights mechanism for privacy-preserving data analysis
- Hardt, Rothblum
- 2010
(Show Context)
Citation Context ...pling function. Data-dependent interactive (as opposed to batch) mechanisms have been considered by Roth and Roughgarden [19], who answer predicate queries on databases with 0-1 entries. Hardt et. al =-=[12]-=- provide a linear time algorithm for the same query and database setting. 7. CONCLUSIONS AND FUTURE WORK We have described an adaptive mechanism for answering complex workloads of counting queries und... |

16 | Differentially private data cubes: optimizing noise sources and consistency
- Ding, Winslett, et al.
- 2011
(Show Context)
Citation Context ...wer a set of wavelet basis queries, while Hay et al. [13] use a hierarchical set of counting queries which recursively decompose the domain. For workloads consisting of sets of marginals, Ding et al. =-=[7]-=- recently proposed a method for selecting an alternative set of marginals, from which the desired counts can be derived. These techniques can each be described in the framework of the recently-propose... |

16 | Differentially private data release through multidimensional partitioning
- Xiao, Xiong, et al.
- 2010
(Show Context)
Citation Context ... the matrix mechanism are independent of the database instance. Recently, a number of data dependent algorithms for answering linear queries under differential privacy have been proposed. Xiao et al. =-=[22]-=- propose a method for computing a strategy matrix using KDtrees, and Cormode et al. [6] propose a related method in which a differentially-private median computation is used to guide hierarchical rang... |

11 | Differentially private spatial decompositions
- Cormode, Procopiuc, et al.
- 2012
(Show Context)
Citation Context ...ta dependent algorithms for answering linear queries under differential privacy have been proposed. Xiao et al. [22] propose a method for computing a strategy matrix using KDtrees, and Cormode et al. =-=[6]-=- propose a related method in which a differentially-private median computation is used to guide hierarchical range queries. While promising, these approaches appear to restrict the strategy to hierarc... |

11 | ireduct: differential privacy with reduced relative errors,” ser
- Xiao, Bender, et al.
- 2011
(Show Context)
Citation Context ... we have shown are suboptimal for many workloads. Dynamic strategy selection can also increase computation cost. These tradeoffs deserve further investigation. Focusing on relative error, Xiao et al. =-=[20]-=- propose a datadependent algorithm to minimize the relative error with an innovative resampling function. Data-dependent interactive (as opposed to batch) mechanisms have been considered by Roth and R... |

3 |
Measuring the achievable error of query sets under differential privacy
- Li, Miklau
(Show Context)
Citation Context ...he input workload. Approximation Rate To bound the approximation rate, we use an existing result showing a lower bound on the optimal error achievable for a workload using the (ɛ, δ)-matrix mechanism =-=[15]-=-. The existence of this bound does not imply an algorithm for achieving it, but it is a useful tool for understanding theoretically and experimentally the quality of the strategies produced by OptStra... |

1 |
consistency: A holistic solution to contingency table release
- Privacy
- 2007
(Show Context)
Citation Context ...is approach focuses on workloads consisting of sets of k-way marginals, for which Barak et al. answer a set of Fourier basis queries using the Laplace mechanism, and then derive the desired marginals =-=[4]-=-. For workloads consisting of all range-count queries over an or-dered domain, two approaches have been proposed. Xiao et al. [21] first answer a set of wavelet basis queries, while Hay et al. [13] u... |

1 |
Optimal design of experiments. Wiley-Interscience
- Pukelsheim
- 1993
(Show Context)
Citation Context ...that sensitivity is measured using the L2 metric (instead of L1) which ultimately allows for better approximate solutions. 2 Second, inspired by the statistical problem of optimal experimental design =-=[5, 18]-=-, we formulate the strategy selection problem as a convex optimization problem which chooses n coefficients to serve as weights for a fixed set of design queries. Third, we show that the eigenvectors ... |