Differentially Private Change-Point Detection

The change-point detection problem seeks to identify distributional changes at an unknown change-point k* in a stream of data. This problem appears in many important practical settings involving personal data, including biosurveillance, fault detection, finance, signal detection, and security systems. The field of differential privacy offers data analysis tools that provide powerful worst-case privacy guarantees. We study the statistical problem of change-point problem through the lens of differential privacy. We give private algorithms for both online and offline change-point detection, analyze these algorithms theoretically, and then provide empirical validation of these results.

[1]  Robert Lund,et al.  Detection of Undocumented Changepoints: A Revision of the Two-Phase Regression Model , 2002 .

[2]  T. Lai.  SEQUENTIAL ANALYSIS: SOME CLASSICAL PROBLEMS AND NEW CHALLENGES , 2001 .

[3]  Yajun Mei,et al.  Is Average Run Length to False Alarm Always an Informative Criterion? , 2008 .

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

[5]  E. Carlstein.  Nonparametric Change-Point Estimation , 1988 .

[6]  M. Pollak.  Optimal Detection of a Change in Distribution , 1985 .

[7]  M. Pollak.  Average Run Lengths of an Optimal Method of Detecting a Change in Distribution. , 1987 .

[8]  A. R. Crathorne,et al.  Economic Control of Quality of Manufactured Product. , 1933 .

[9]  G. Moustakides.  Optimal stopping times for detecting changes in distributions , 1986 .

[10]  T. Lai.  Sequential changepoint detection in quality control and dynamical systems , 1995 .

[11]  Hock Peng Chan,et al.  Optimal sequential detection in multi-stream data , 2015, 1506.08504.

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

[13]  S. W. Roberts.  A Comparison of Some Control Chart Procedures , 1966 .

[14]  Martin Kulldorff,et al.  Prospective time periodic geographical disease surveillance using a scan statistic , 2001 .

[15]  David Siegmund,et al.  MODEL SELECTION FOR HIGH-DIMENSIONAL, MULTI-SEQUENCE CHANGE-POINT PROBLEMS , 2012 .

[16]  S. Panchapakesan,et al.  Inference about the Change-Point in a Sequence of Random Variables: A Selection Approach , 1988 .

[17]  P. Perron,et al.  Computation and Analysis of Multiple Structural-Change Models , 1998 .

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

[19]  G. Lorden.  PROCEDURES FOR REACTING TO A CHANGE IN DISTRIBUTION , 1971 .

[20]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[21]  Y. Mei.  Efficient scalable schemes for monitoring a large number of data streams , 2010 .

[22]  A. Shiryaev.  On Optimum Methods in Quickest Detection Problems , 1963 .

[23]  Y. Mei.  Sequential change-point detection when unknown parameters are present in the pre-change distribution , 2006, math/0605322.

[24]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .