Differentially Private Chi-squared Test by Unit Circle Mechanism

This paper develops differentially private mechanisms for χ2 test of independence. While existing works put their effort into properly controlling the type-I error, in addition to that, we investigate the type-II error of differentially private mechanisms. Based on the analysis, we present unit circle mechanism: a novel differentially private mechanism based on the geometrical property of the test statistics. Compared to existing output perturbation mechanisms, our mechanism improves the dominated term of the type-II error from O(1) to O(exp(− √ N)) where N is the sample size. Furthermore, we introduce novel procedures for multiple χ2 tests by incorporating the unit circle mechanism into the sparse vector technique and the exponential mechanism. These procedures can control the family-wise error rate (FWER) properly, which has never been attained by existing mechanisms.

[1]  Vitaly Shmatikov,et al.  Privacy-preserving data exploration in genome-wide association studies , 2013, KDD.

[2]  Aaron Roth,et al.  The Algorithmic Foundations of Differential Privacy , 2014, Found. Trends Theor. Comput. Sci..

[3]  Ryan M. Rogers,et al.  Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing , 2016, ICML 2016.

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

[5]  Yue Wang,et al.  Differentially Private Hypothesis Testing, Revisited , 2015, ArXiv.

[6]  Stephen E. Fienberg,et al.  Scalable privacy-preserving data sharing methodology for genome-wide association studies , 2014, J. Biomed. Informatics.

[7]  Yue Wang,et al.  Maximum Likelihood Postprocessing for Differential Privacy under Consistency Constraints , 2015, KDD.

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

[9]  Geoffrey I. Webb,et al.  A Multiple Test Correction for Streams and Cascades of Statistical Hypothesis Tests , 2016, KDD.

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

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

[12]  Bonnie Berger,et al.  Realizing privacy preserving genome-wide association studies , 2016, Bioinform..

[13]  Katrina Ligett,et al.  A Simple and Practical Algorithm for Differentially Private Data Release , 2010, NIPS.

[14]  Stephen E. Fienberg,et al.  Privacy-Preserving Data Sharing for Genome-Wide Association Studies , 2012, J. Priv. Confidentiality.

[15]  Constantinos Daskalakis,et al.  Priv'IT: Private and Sample Efficient Identity Testing , 2017, ICML.

[16]  Stephen E. Fienberg,et al.  Privacy Preserving GWAS Data Sharing , 2011, 2011 IEEE 11th International Conference on Data Mining Workshops.

[17]  Marco Gaboardi,et al.  Dual Query: Practical Private Query Release for High Dimensional Data , 2014, ICML.

[18]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[19]  Cynthia Dwork,et al.  Privacy, accuracy, and consistency too: a holistic solution to contingency table release , 2007, PODS.

[20]  Ninghui Li,et al.  Understanding the Sparse Vector Technique for Differential Privacy , 2016, Proc. VLDB Endow..