Adaptive estimation with change detection for streaming data

[1]  Gyo-Young Cho,et al.  Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix , 2006 .

[2]  Iyad A. Ajwa,et al.  Grobner Bases Algorithm , 1995 .

[3]  Daniel W. Apley,et al.  An Optimal Filter Design Approach to Statistical Process Control , 2007 .

[4]  Joe H. Sullivan,et al.  Detection of Multiple Change Points from Clustering Individual Observations , 2002 .

[5]  David S. Moore,et al.  Unified Large-Sample Theory of General Chi-Squared Statistics for Tests of Fit , 1975 .

[6]  J. Healy A note on multivariate CUSUM procedures , 1987 .

[7]  John F. MacGregor STATISTICAL PROCESS CONTROL OF MULTIVARIATE PROCESSES , 1994 .

[8]  T. R. Fortescue,et al.  Implementation of self-tuning regulators with variable forgetting factors , 1981, Autom..

[9]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .

[10]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[11]  H. Fairfield Smith,et al.  The problem of comparing the result of two experiments with unequal errors , 1936 .

[12]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[13]  Mark Crovella,et al.  Mining anomalies using traffic feature distributions , 2005, SIGCOMM '05.

[14]  Douglas M. Hawkins,et al.  The Changepoint Model for Statistical Process Control , 2003 .

[15]  Niall M. Adams,et al.  Adaptive Change Detection for Relay-Like Behaviour , 2014, 2014 IEEE Joint Intelligence and Security Informatics Conference.

[16]  F. Gan Joint monitoring of process mean and variance using exponentially weighted moving average control charts , 1995 .

[17]  H. Hotelling Multivariate Quality Control-illustrated by the air testing of sample bombsights , 1947 .

[18]  Jaeheon Lee,et al.  The Design of GLR Control Charts for Monitoring the Process Mean and Variance , 2013 .

[19]  M. Abliz Internet Denial of Service Attacks and Defense Mechanisms , 2011 .

[20]  E. Suchman,et al.  The American Soldier: Adjustment During Army Life. , 1949 .

[21]  Kaibo Wang,et al.  Adaptive Charting Techniques: Literature Review and Extensions , 2010 .

[22]  Bodhini R. Jayasuriya,et al.  Testing for Polynomial Regression Using Nonparametric Regression Techniques , 1996 .

[23]  M. C. Spruill,et al.  A Comparison of Chi-Square Goodness-of-Fit Tests Based on Approximate Bahadur Slope , 1976 .

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

[25]  Michael Buckley,et al.  AN APPROXIMATION TO THE DISTRIBUTION OF QUADRATIC FORMS IN NORMAL RANDOM VARIABLES , 1988 .

[26]  Joe H. Sullivan,et al.  A Self-Starting Control Chart for Multivariate Individual Observations , 2002, Technometrics.

[27]  Zhonghua Li,et al.  A multivariate control chart for simultaneously monitoring process mean and variability , 2010, Comput. Stat. Data Anal..

[28]  E. Suchman,et al.  The American soldier: Adjustment during army life. (Studies in social psychology in World War II), Vol. 1 , 1949 .

[29]  Victor Tercero-Gomez,et al.  A Self‐Starting CUSUM Chart Combined with a Maximum Likelihood Estimator for the Time of a Detected Shift in the Process Mean , 2014, Qual. Reliab. Eng. Int..

[30]  Rudolf B. Blazek,et al.  Detection of intrusions in information systems by sequential change-point methods , 2005 .

[31]  H. Robbins,et al.  Application of the Method of Mixtures to Quadratic Forms in Normal Variates , 1949 .

[32]  P. Maravelakis,et al.  A CUSUM control chart for monitoring the variance when parameters are estimated , 2011 .

[33]  Pedro Casas,et al.  Optimal volume anomaly detection and isolation in large-scale IP networks using coarse-grained measurements , 2010, Comput. Networks.

[34]  Ratul Mahajan,et al.  Controlling high bandwidth aggregates in the network , 2002, CCRV.

[35]  Jennifer Widom,et al.  Models and issues in data stream systems , 2002, PODS.

[36]  George C. Runger,et al.  Comparison of multivariate CUSUM charts , 1990 .

[37]  Marianne Frisén Statistical measures for evaluation of methods for syndromic surveillance , 2003 .

[38]  W. Shewhart The Economic Control of Quality of Manufactured Product. , 1932 .

[39]  F. Choobineh,et al.  Control-Limits of QC Charts for Skewed Distributions Using Weighted-Variance , 1987, IEEE Transactions on Reliability.

[40]  F. E. Satterthwaite An approximate distribution of estimates of variance components. , 1946, Biometrics.

[41]  David Siegmund,et al.  Sequential multi-sensor change-point detection , 2013, 2013 Information Theory and Applications Workshop (ITA).

[42]  Marco de Vivo,et al.  A review of port scanning techniques , 1999, CCRV.

[43]  Charles W. Champ,et al.  The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters , 2001, Technometrics.

[44]  Testing goodness of fit of polynomial models via spline smoothing techniques , 1994 .

[45]  Sudipto Guha,et al.  Streaming-data algorithms for high-quality clustering , 2002, Proceedings 18th International Conference on Data Engineering.

[46]  Scott E. Hein,et al.  Modeling volatility changes in the 10-year Treasury , 2006 .

[47]  Léon Bottou,et al.  Stochastic Learning , 2003, Advanced Lectures on Machine Learning.

[48]  Ramon C. Littell,et al.  Asymptotic Optimality of Fisher's Method of Combining Independent Tests , 1971 .

[49]  Arjun K. Gupta,et al.  Testing and Locating Variance Changepoints with Application to Stock Prices , 1997 .

[50]  Douglas M. Hawkins,et al.  A Multivariate Change-Point Model for Change in Mean Vector and/or Covariance Structure , 2009 .

[51]  F. Famoye Continuous Univariate Distributions, Volume 1 , 1994 .

[52]  Simon Haykin,et al.  Adaptive Filter Theory 4th Edition , 2002 .

[53]  Marianne Frisén,et al.  Statistical Surveillance. Optimality and Methods , 2003 .

[54]  Douglas M. Hawkins,et al.  Self-Starting Multivariate Exponentially Weighted Moving Average Control Charting , 2007, Technometrics.

[55]  Charles W. Champ,et al.  Effects of Parameter Estimation on Control Chart Properties: A Literature Review , 2006 .

[56]  M. Whitlock Combining probability from independent tests: the weighted Z‐method is superior to Fisher's approach , 2005, Journal of evolutionary biology.

[57]  M. Lavielle,et al.  Detection of multiple change-points in multivariate time series , 2006 .

[58]  Kirk D. Borne,et al.  Scalable, asynchronous, distributed eigen monitoring of astronomy data streams , 2011, Stat. Anal. Data Min..

[59]  Peter Hall Chi Squared Approximations to the Distribution of a Sum of Independent Random Variables , 1983 .

[60]  Z Chen,et al.  Is the weighted z‐test the best method for combining probabilities from independent tests? , 2011, Journal of evolutionary biology.

[61]  Prabhakar Raghavan,et al.  Computing on data streams , 1999, External Memory Algorithms.

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

[63]  Roger Sauter,et al.  Introduction to Probability and Statistics for Engineers and Scientists , 2005, Technometrics.

[64]  Douglas M. Hawkins,et al.  The CUSUM and the EWMA Head-to-Head , 2014 .

[65]  D. R. Jensen,et al.  A Gaussian Approximation to the Distribution of a Definite Quadratic Form , 1972 .

[66]  Niall M. Adams,et al.  Continuous Monitoring of a Computer Network Using Multivariate Adaptive Estimation , 2013, 2013 IEEE 13th International Conference on Data Mining Workshops.

[67]  J. Imhof Computing the distribution of quadratic forms in normal variables , 1961 .

[68]  Douglas M. Hawkins,et al.  A General Multivariate Exponentially Weighted Moving-Average Control Chart , 2007 .

[69]  Monika Ritsch-Marte,et al.  A new method for change-point detection developed for on-line analysis of the heart beat variability during sleep , 2005 .

[70]  J. G. Saw,et al.  Chebyshev Inequality With Estimated Mean and Variance , 1984 .

[71]  M. Kendall Statistical Methods for Research Workers , 1937, Nature.

[72]  Gyo-Young Cho,et al.  Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix with Variable Sampling Intervals , 2011 .

[73]  R. Davies The distribution of a linear combination of 2 random variables , 1980 .

[74]  Geoff Hulten,et al.  Mining time-changing data streams , 2001, KDD '01.

[75]  Jelena Mirkovic,et al.  Attacking DDoS at the source , 2002, 10th IEEE International Conference on Network Protocols, 2002. Proceedings..

[76]  R. Farebrother The Distribution of a Positive Linear Combination of X2 Random Variables , 1984 .

[77]  Bruce G. Lindsay,et al.  Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications , 2000 .

[78]  Vern Paxson,et al.  Bro: a system for detecting network intruders in real-time , 1998, Comput. Networks.

[79]  Morton B. Brown 400: A Method for Combining Non-Independent, One-Sided Tests of Significance , 1975 .

[80]  Douglas M. Hawkins CUMULATIVE SUM CONTROL CHARTING: AN UNDERUTILIZED SPC TOOL , 1993 .

[81]  William H. Woodall,et al.  Performance Metrics for Surveillance Schemes , 2008 .

[82]  Dimitris K. Tasoulis,et al.  Nonparametric Monitoring of Data Streams for Changes in Location and Scale , 2011, Technometrics.

[83]  B. L. Welch THE SIGNIFICANCE OF THE DIFFERENCE BETWEEN TWO MEANS WHEN THE POPULATION VARIANCES ARE UNEQUAL , 1938 .

[84]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[85]  Gregory F Cooper,et al.  Issues in applied statistics for public health bioterrorism surveillance using multiple data streams: research needs , 2007, Statistics in medicine.

[86]  J. Sheil,et al.  The Distribution of Non‐Negative Quadratic Forms in Normal Variables , 1977 .

[87]  Charles W. Champ,et al.  Exact results for shewhart control charts with supplementary runs rules , 1987 .

[88]  Eric Gilbert,et al.  A statistical framework for streaming graph analysis , 2013, 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2013).

[89]  Lennart Ljung,et al.  Theory and applications of self-tuning regulators , 1977, Autom..

[90]  G. Box Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification , 1954 .

[91]  S. W. Roberts Control chart tests based on geometric moving averages , 2000 .

[92]  Satterthwaite Fe An approximate distribution of estimates of variance components. , 1946 .

[93]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[94]  E Peizer,et al.  Technical aids. , 1978, Prosthetics and orthotics international.

[95]  Cedric E. Ginestet ggplot2: Elegant Graphics for Data Analysis , 2011 .

[96]  A. W. Davis A Differential Equation Approach to Linear Combinations of Independent Chi-Squares , 1977 .

[97]  Douglas M. Hawkins,et al.  Detection of multiple change-points in multivariate data , 2013 .

[98]  Christoforos Anagnostopoulos,et al.  Online linear and quadratic discriminant analysis with adaptive forgetting for streaming classification , 2012, Stat. Anal. Data Min..

[99]  Niall M. Adams,et al.  A comparison of efficient approximations for a weighted sum of chi-squared random variables , 2016, Stat. Comput..

[100]  York Marcel Dekker The State of Statistical Process Control as We Proceed into the 21st Century , 2000 .

[101]  Zhonghua Li,et al.  Self-starting control chart for simultaneously monitoring process mean and variance , 2010 .

[102]  L. Lee,et al.  Updated guidelines for evaluating public health surveillance systems: recommendations from the Guidelines Working Group. , 2001, MMWR. Recommendations and reports : Morbidity and mortality weekly report. Recommendations and reports.

[103]  Charles W. Champ,et al.  A multivariate exponentially weighted moving average control chart , 1992 .

[104]  Marion R. Reynolds,et al.  A GLR Control Chart for Monitoring the Mean Vector of a Multivariate Normal Process , 2013 .

[105]  Fredrik Gustafsson,et al.  Adaptive filtering and change detection , 2000 .

[106]  J. Uspensky Introduction to mathematical probability , 1938 .

[107]  H. Solomon,et al.  Distribution of a Sum of Weighted Chi-Square Variables , 1977 .

[108]  D. Hawkins Self‐Starting Cusum Charts for Location and Scale , 1987 .

[109]  Giovanna Capizzi,et al.  An Adaptive Exponentially Weighted Moving Average Control Chart , 2003, Technometrics.

[110]  Hari Balakrishnan,et al.  Fast portscan detection using sequential hypothesis testing , 2004, IEEE Symposium on Security and Privacy, 2004. Proceedings. 2004.

[111]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[112]  Niall M. Adams,et al.  Two Nonparametric Control Charts for Detecting Arbitrary Distribution Changes , 2012 .

[113]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[114]  James M. Lucas,et al.  Exponentially weighted moving average control schemes: Properties and enhancements , 1990 .

[115]  David J. Hand,et al.  Statistical Techniques for Fraud Detection, Prevention and Assessment , 2007, NATO ASI Mining Massive Data Sets for Security.

[116]  Jin-Ting Zhang,et al.  Statistical inferences for functional data , 2007, 0708.2207.

[117]  P. Patnaik THE NON-CENTRAL χ2- AND F-DISTRIBUTIONS AND THEIR APPLICATIONS , 1949 .

[118]  A. Castaño-Martínez,et al.  Distribution of a sum of weighted noncentral chi-square variables , 2005 .

[119]  Jesús S. Aguilar-Ruiz,et al.  Knowledge discovery from data streams , 2009, Intell. Data Anal..

[120]  Bruno Buchberger,et al.  Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[121]  J. Macgregor,et al.  The exponentially weighted moving variance , 1993 .

[122]  Hongjoong Kim,et al.  A novel approach to detection of intrusions in computer networks via adaptive sequential and batch-sequential change-point detection methods , 2006, IEEE Transactions on Signal Processing.

[123]  Donghui Zhang,et al.  Online event-driven subsequence matching over financial data streams , 2004, SIGMOD '04.

[124]  R. Berk,et al.  Continuous Univariate Distributions, Volume 2 , 1995 .

[125]  Peihua Qiu,et al.  Multivariate Statistical Process Control Using LASSO , 2009 .

[126]  Robert K. Cunningham,et al.  A taxonomy of computer worms , 2003, WORM '03.

[127]  Wei Jiang,et al.  Adaptive CUSUM procedures with EWMA-based shift estimators , 2008 .

[128]  In-Beum Lee,et al.  Adaptive multivariate statistical process control for monitoring time-varying processes , 2006 .

[129]  Pierre Lafaye de Micheaux,et al.  Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods , 2010, Comput. Stat. Data Anal..

[130]  Juan E. Tapiador,et al.  Anomaly detection methods in wired networks: a survey and taxonomy , 2004, Comput. Commun..

[131]  James M. Lucas,et al.  The Design and Use of V-Mask Control Schemes , 1976 .

[132]  S. Kent,et al.  On the trail of intrusions into information systems , 2000 .

[133]  B. Mark On Self Tuning Regulators , 1972 .

[134]  P. Bentler,et al.  Corrections to test statistics in principal Hessian directions , 2000 .

[135]  W. Woodall,et al.  Multivariate CUSUM Quality- Control Procedures , 1985 .

[136]  Martin Roesch,et al.  Snort - Lightweight Intrusion Detection for Networks , 1999 .

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

[138]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

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

[140]  Alexander G. Tartakovsky,et al.  On optimality of the Shiryaev-Roberts procedure for detecting a change in distribution , 2009, 0904.3370.

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

[142]  T. Pham-Gia,et al.  The generalized beta- and F-distributions in statistical modelling , 1989 .

[143]  Aiko Pras,et al.  Autonomic Parameter Tuning of Anomaly-Based IDSs: an SSH Case Study , 2012, IEEE Transactions on Network and Service Management.

[144]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[145]  J Coberly,et al.  Public health monitoring tools for multiple data streams. , 2005, MMWR supplements.

[146]  Douglas M. Hawkins,et al.  Self-Starting Multivariate Control Charts for Location and Scale , 2011 .

[147]  P. Fearnhead,et al.  Optimal detection of changepoints with a linear computational cost , 2011, 1101.1438.

[148]  Shai Ben-David,et al.  Detecting Change in Data Streams , 2004, VLDB.

[149]  P. Patnaik The Non-central X^2- and F- distribution and Their Applications , 1949 .

[150]  Giovanna Capizzi,et al.  Self-Starting CUSCORE Control Charts for Individual Multivariate Observations , 2010 .

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

[152]  Alexander G. Tartakovsky,et al.  A novel approach to detection of \denial{of{service" attacks via adaptive sequential and batch{sequential change{point detection methods , 2001 .

[153]  Thomer M. Gil MULTOPS: a data structure for denial-of-service attack detection , 2000 .

[154]  Douglas M. Hawkins,et al.  A Multivariate Change-Point Model for Statistical Process Control , 2006, Technometrics.

[155]  A. Wood An F Approximation to the Distribution of a Linear Combination of Chi-squared Variables. , 1989 .

[156]  Christopher Nemeth,et al.  Sequential Monte Carlo Methods for State and Parameter Estimation in Abruptly Changing Environments , 2014, IEEE Transactions on Signal Processing.

[157]  Marion R. Reynolds,et al.  Multivariate Control Charts for Monitoring the Process Mean and Variability Using Sequential Sampling , 2007 .

[158]  Giovanna Capizzi,et al.  Adaptive Generalized Likelihood Ratio Control Charts for Detecting Unknown Patterned Mean Shifts , 2012 .

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

[160]  R. Crosier Multivariate generalizations of cumulative sum quality-control schemes , 1988 .

[161]  Douglas M. Hawkins,et al.  A Change-Point Model for a Shift in Variance , 2005 .

[162]  Marc S. Paolella Intermediate Probability: A Computational Approach , 2007 .

[163]  J. Kost,et al.  Combining dependent P-values , 2002 .

[164]  Idris A. Eckley,et al.  changepoint: An R Package for Changepoint Analysis , 2014 .

[165]  Fugee Tsung,et al.  A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes , 2003 .