Locating a Small Cluster Privately

We present a new algorithm for locating a small cluster of points with differential privacy [Dwork, McSherry, Nissim, and Smith, 2006]. Our algorithm has implications to private data exploration, clustering, and removal of outliers. Furthermore, we use it to significantly relax the requirements of the sample and aggregate technique [Nissim, Raskhodnikova, and Smith, 2007], which allows compiling of "off the shelf" (non-private) analyses into analyses that preserve differential privacy.

[1]  Guy N. Rothblum,et al.  Boosting and Differential Privacy , 2010, 2010 IEEE 51st Annual Symposium on Foundations of Computer Science.

[2]  Amos Beimel,et al.  Private Learning and Sanitization: Pure vs. Approximate Differential Privacy , 2013, APPROX-RANDOM.

[3]  Toniann Pitassi,et al.  Preserving Statistical Validity in Adaptive Data Analysis , 2014, STOC.

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

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

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

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

[8]  Adam D. Smith,et al.  Differentially Private Feature Selection via Stability Arguments, and the Robustness of the Lasso , 2013, COLT.

[9]  Adam D. Smith,et al.  Privacy-preserving statistical estimation with optimal convergence rates , 2011, STOC '11.

[10]  Daniel A. Spielman,et al.  Spectral Graph Theory and its Applications , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[11]  Moni Naor,et al.  Our Data, Ourselves: Privacy Via Distributed Noise Generation , 2006, EUROCRYPT.

[12]  Salil P. Vadhan,et al.  The Complexity of Differential Privacy , 2017, Tutorials on the Foundations of Cryptography.

[13]  Cynthia Dwork,et al.  Differential privacy and robust statistics , 2009, STOC '09.

[14]  Kasturi R. Varadarajan,et al.  Geometric Approximation via Coresets , 2007 .

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

[16]  Moni Naor,et al.  On the complexity of differentially private data release: efficient algorithms and hardness results , 2009, STOC '09.

[17]  Raef Bassily,et al.  Algorithmic stability for adaptive data analysis , 2015, STOC.

[18]  Kobbi Nissim,et al.  Differentially Private Release and Learning of Threshold Functions , 2015, 2015 IEEE 56th Annual Symposium on Foundations of Computer Science.

[19]  V. V. Shenmaier,et al.  The problem of a minimal ball enclosing k points , 2013 .

[20]  Sofya Raskhodnikova,et al.  What Can We Learn Privately? , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

[21]  P. Massart,et al.  Adaptive estimation of a quadratic functional by model selection , 2000 .