Calibrating Data to Sensitivity in Private Data Analysis

We present an approach to differentially private computation in which one does not scale up the magnitude of noise for challenging queries, but rather scales down the contributions of challenging records. While scaling down all records uniformly is equivalent to scaling up the noise magnitude, we show that scaling records non-uniformly can result in substantially higher accuracy by bypassing the worst-case requirements of differential privacy for the noise magnitudes. This paper details the data analysis platform wPINQ, which generalizes the Privacy Integrated Query (PINQ) to weighted datasets. Using a few simple operators (including a non-uniformly scaling Join operator) wPINQ can reproduce (and improve) several recent results on graph analysis and introduce new generalizations (e.g., counting triangles with given degrees). We also show how to integrate probabilistic inference techniques to synthesize datasets respecting more complicated (and less easily interpreted) measurements.

[1]  Matthew Richardson,et al.  Trust Management for the Semantic Web , 2003, SEMWEB.

[2]  Priya Mahadevan,et al.  Systematic topology analysis and generation using degree correlations , 2006, SIGCOMM 2006.

[3]  Cynthia Dwork,et al.  Calibrating Noise to Sensitivity in Private Data Analysis , 2006, TCC.

[4]  Sofya Raskhodnikova,et al.  Smooth sensitivity and sampling in private data analysis , 2007, STOC '07.

[5]  Christos Faloutsos,et al.  Graph evolution: Densification and shrinking diameters , 2006, TKDD.

[6]  Kunal Talwar,et al.  Mechanism Design via Differential Privacy , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[7]  Dan Suciu,et al.  Relationship privacy: output perturbation for queries with joins , 2009, PODS.

[8]  Frank McSherry,et al.  Privacy integrated queries: an extensible platform for privacy-preserving data analysis , 2009, SIGMOD Conference.

[9]  J. Leeuw,et al.  Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods , 2009 .

[10]  David D. Jensen,et al.  Accurate Estimation of the Degree Distribution of Private Networks , 2009, 2009 Ninth IEEE International Conference on Data Mining.

[11]  Vitaly Shmatikov,et al.  Airavat: Security and Privacy for MapReduce , 2010, NSDI.

[12]  Benjamin C. Pierce,et al.  Distance makes the types grow stronger: a calculus for differential privacy , 2010, ICFP '10.

[13]  Frank McSherry,et al.  Probabilistic Inference and Differential Privacy , 2010, NIPS.

[14]  Andrew McGregor,et al.  Optimizing linear counting queries under differential privacy , 2009, PODS.

[15]  Andreas Haeberlen,et al.  Differential Privacy Under Fire , 2011, USENIX Security Symposium.

[16]  Jian Pei,et al.  Privacy-aware data management in information networks , 2011, SIGMOD '11.

[17]  Ben Y. Zhao,et al.  Sharing graphs using differentially private graph models , 2011, IMC '11.

[18]  Gerome Miklau,et al.  An Adaptive Mechanism for Accurate Query Answering under Differential Privacy , 2012, Proc. VLDB Endow..

[19]  Yang Xiang,et al.  On Learning Cluster Coefficient of Private Networks , 2012, ASONAM.

[20]  Elaine Shi,et al.  GUPT: privacy preserving data analysis made easy , 2012, SIGMOD Conference.

[21]  Sharon Goldberg,et al.  A workflow for differentially-private graph synthesis , 2012, WOSN '12.

[22]  Shuigeng Zhou,et al.  Recursive mechanism: towards node differential privacy and unrestricted joins , 2013, SIGMOD '13.

[23]  A. Barabasi,et al.  Network science , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[24]  Sofya Raskhodnikova,et al.  Analyzing Graphs with Node Differential Privacy , 2013, TCC.

[25]  Avrim Blum,et al.  Differentially private data analysis of social networks via restricted sensitivity , 2012, ITCS '13.

[26]  Andreas Haeberlen,et al.  Linear dependent types for differential privacy , 2013, POPL.

[27]  Sofya Raskhodnikova,et al.  Private analysis of graph structure , 2011, Proc. VLDB Endow..