Hot-spots detection in count data by Poisson assisted smooth sparse tensor decomposition

References

• A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM. J. Imaging. Sci. 2 (2009), pp. 183–202.
   Web of Science ®Google Scholar
• L.M. Brègman, Relaxation method for finding a common point of convex sets and its application to optimization problems, Doklady Akademii Nauk. 171 (1966), pp. 1019–1022. Russian Academy of Sciences.
   Web of Science ®Google Scholar
• J. Chen and F. Fang, Semiparametric likelihood for estimating equations with non-ignorable non-response by non-response instrument, J. Nonparametr. Stat. 31 (2019), pp. 420–434.
   Web of Science ®Google Scholar
• J. Chen, F. Fang, and Z. Xiao, Semiparametric inference for estimating equations with nonignorably missing covariates, J. Nonparametr. Stat. 30 (2018a), pp. 796–812.
   Web of Science ®Google Scholar
• J. Chen, J. Shao, and F. Fang, Instrument search in pseudo-likelihood approach for nonignorable nonresponse, Ann. Inst. Stat. Math. 73 (2021a), pp. 519–533.
   Web of Science ®Google Scholar
• J. Chen, B. Xie, and J. Shao, Pseudo likelihood and dimension reduction for data with nonignorable nonresponse, Stat. Theory Relat. Fields. 2 (2018b), pp. 196–205.
   Google Scholar
• Q. Chen, J. Chen, Y. Zhou, L. Huang, Y. Tang, J. Li, and J. Zhang, Natural history and associated early life factors of childhood asthma: A population registry-based cohort study in denmark, BMJ. Open. 11 (2021b), pp. e045728.
   PubMed Web of Science ®Google Scholar
• D. Conesa, M. Martínez-Beneito, R. Amorós, and A. López-Quílez, Bayesian hierarchical poisson models with a hidden markov structure for the detection of influenza epidemic outbreaks, Stat. Methods. Med. Res. 24 (2015), pp. 206–223.
   PubMed Web of Science ®Google Scholar
• I. Daubechies, M. Defrise, and C. De Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Commun. Pure Appl. Math.: A Journal Issued by the Courant Institute of Mathematical Sciences 57 (2004), pp. 1413–1457.
   Web of Science ®Google Scholar
• B. De Ketelaere, M. Hubert, and E. Schmitt, Overview of PCA-based statistical process-monitoring methods for time-dependent, high-dimensional data, J. Qual. Technol. 47 (2015), pp. 318–335.
   Web of Science ®Google Scholar
• M.E. Eren, J.S. Moore, and B.S Alexandro, Multi-dimensional anomalous entity detection via poisson tensor factorization, 2020 IEEE International Conference on Intelligence and Security Informatics (ISI), IEEE, 2020, pp. 1–6.
   Google Scholar
• J. Friedman, T. Hastie, and R. Tibshirani, The Elements of Statistical Learning, Vol. 1, Springer series in statistics New York, 1, Springer, New York, 2001.
   Google Scholar
• J. Friedman, T. Hastie, and R. Tibshirani, Regularization paths for generalized linear models via coordinate descent, J. Stat. Softw. 33 (2010), pp. 1.
   PubMed Web of Science ®Google Scholar
• M.R. Gahrooei, H. Yan, K. Paynabar, and J. Shi, Multiple tensor-on-tensor regression: An approach for modeling processes with heterogeneous sources of data, Technometrics 63 (2021), pp. 147–159.
   Web of Science ®Google Scholar
• S.W. Han, K. -L. Tsui, B. Ariyajunya, and S.B. Kim, A comparison of cusum, ewma, and temporal scan statistics for detection of increases in poisson rates, Qual. Reliab. Eng. Int. 26 (2010), pp. 279–289.
   Web of Science ®Google Scholar
• T. Hastie, R. Tibshirani, and M. Wainwright, Statistical Learning with Sparsity: The Lasso and Generalizations, CRC Press, 2015.
   Google Scholar
• D.M. Hawkins, Regression adjustment for variables in multivariate quality control, J. Qual. Technol. 25 (1993), pp. 170–182.
   Web of Science ®Google Scholar
• F.L. Hitchcock, The expression of a tensor or a polyadic as a sum of products, J. Math. Phys. 6 (1927), pp. 164–189.
   Google Scholar
• L Hunyadi, B-splines. 2020. Available at https://www.mathworks.com/matlabcentral/fileexchange/27374-b-splines.
   Google Scholar
• A. Ihler, J. Hutchins, and P Smyth, Adaptive event detection with time-varying poisson processes, Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2006, pp. 207–216.
   Google Scholar
• R. Killick and I. Eckley, Changepoint: An R package for changepoint analysis, J. Stat. Softw. 58 (2014), pp. 1–19.
   Web of Science ®Google Scholar
• M.H. Kim and M.G. Akritas, Order thresholding, Ann. Stat. 38 (2010), pp. 2314–2350.
   Web of Science ®Google Scholar
• T.G. Kolda and B.W. Bader, Tensor decompositions and applications, SIAM Rev. 51 (2009), pp. 455–500.
   Web of Science ®Google Scholar
• S. Kullback and R.A. Leibler, On information and sufficiency, Ann. Math. Stat. 22 (1951), pp. 79–86.
   Google Scholar
• M. Kulldorff, A spatial scan statistic, Commun. Stat.-Theor. Meth. 26 (1997), pp. 1481–1496.
   Web of Science ®Google Scholar
• M. Kulldorff, Prospective time periodic geographical disease surveillance using a scan statistic, J. R. Stat. Soc.: Ser. A (Stat. Soc.). 164 (2001), pp. 61–72.
   Web of Science ®Google Scholar
• M. Kulldorff, L. Huang, and K. Konty, A scan statistic for continuous data based on the normal probability model, Int. J. Health. Geogr. 8 (2009), pp. 1–9.
   PubMed Web of Science ®Google Scholar
• M. Kulldorff and N. Nagarwalla, Spatial disease clusters: Detection and inference, Stat. Med. 14 (1995), pp. 799–810.
   PubMed Web of Science ®Google Scholar
• K. Liu, R. Zhang, and Y. Mei, Scalable sum-shrinkage schemes for distributed monitoring large-scale data streams, Stat. Sin. 29 (2019), pp. 1–22.
   Web of Science ®Google Scholar
• Lorden, Procedures for reacting to a change in distribution, Ann. Math. Stat. 42 (1971), pp. 1897–1908.
   Google Scholar
• H. Nagaraja, Some nondegenerate limit laws for the selection differential, Ann. Stat. 10 (1982), pp. 1306–1310.
   Web of Science ®Google Scholar
• J.I. Naus, Clustering of Random Points in Line and Plane, Harvard University Press, 1963.
   Google Scholar
• D. Neill, A. Moore, and G. Cooper, A Bayesian spatial scan statistic, Adv. Neural. Inf. Process. Syst. 18 (2005), pp. 1003–1010.
   Google Scholar
• D.B. Neill, A.W. Moore, and G.F. Cooper, A Bayesian spatial scan statistic, Adv. Neural. Inf. Process. Syst. 18 (2006), pp. 1003–1010.
   Google Scholar
• E.S. Page, Continuous inspection schemes, Biometrika 4/1 (1954), pp. 100–115.
   Google Scholar
• K. Paynabar, J. Jin, and M. Pacella, Monitoring and diagnosis of multichannel nonlinear profile variations using uncorrelated multilinear principal component analysis, IIE. Trans. 45 (2013), pp. 1235–1247.
   Web of Science ®Google Scholar
• J. Pinheiro and D. Bates, Mixed-effects Models in S and S-PLUS, Springer Science & Business Media, 2006.
   Google Scholar
• N.G. Polson, J.G. Scott, and B.T. Willard, Proximal algorithms in statistics and machine learning, Stat. Sci. 30 (2015), pp. 559–581.
   Web of Science ®Google Scholar
• P. Qiu, Introduction to Statistical Process Control, Chapman and Hall/CRC, 2013.
   Google Scholar
• D. Ruppert, Selecting the number of knots for penalized splines, J. Comput. Graph. Stat. 11 (2002), pp. 735–757.
   Web of Science ®Google Scholar
• T. Tango, K. Takahashi, and K. Kohriyama, A space–time scan statistic for detecting emerging outbreaks, Biometrics 67 (2011), pp. 106–115.
   PubMed Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the lasso, J. R. Stat. Soc. Ser. B (Methodol.) 58 (1996), pp. 267–288.
   Google Scholar
• M. Turcotte, J. Moore, N. Heard, and A McPhall, Poisson factorization for peer-based anomaly detection, 2016 IEEE Conference on Intelligence and Security Informatics (ISI), IEEE, 2016, pp. 208–210.
   Google Scholar
• H. Yan, K. Paynabar, and J. Shi, Image-based process monitoring using low-rank tensor decomposition, IEEE. Trans. Autom. Sci. Eng. 12 (2014), pp. 216–227.
   Web of Science ®Google Scholar
• H. Yan, K. Paynabar, and J. Shi, Anomaly detection in images with smooth background via smooth-sparse decomposition, Technometrics 59 (2017), pp. 102–114.
   Web of Science ®Google Scholar
• H. Yan, K. Paynabar, and J. Shi, Real-time monitoring of high-dimensional functional data streams via spatio-temporal smooth sparse decomposition, Technometrics 60 (2018a), pp. 181–197.
   Web of Science ®Google Scholar
• H. Yan, K. Paynabar, and J. Shi, Real-time monitoring of high-dimensional functional data streams via spatio-temporal smooth sparse decomposition, Technometrics 60 (2018b), pp. 181–197.
   Web of Science ®Google Scholar
• Y Zhao, New progress in hot-spots detection, partial-differential-equation-based model identification and statistical computation, PhD thesis, Georgia Institute of Technology, 2021.
   Google Scholar
• Y. Zhao, and X Huo, A homotopic method to solve the lasso problems with an improved upper bound of convergence rate, preprint (2020). Available at arXiv:2010.13934.
   Google Scholar
• Y. Zhao, X. Huo, and Y Mei, Identification of underlying dynamic system from noisy data with splines, preprint (2021a). Available at arXiv:2103.10231.
   Google Scholar
• Y. Zhao, H. Yan, S. Holte, and Y. Mei, Rapid detection of hot-spots via tensor decomposition with applications to crime rate data, J. Appl. Stat. 49 (2021b), pp. 1–27.
   Web of Science ®Google Scholar
• Y. Zhao, H. Yan, S.E. Holte, R.P. Kerani, and Y Mei, Rapid detection of hot-spot by tensor decomposition with application to weekly gonorrhea data, International Workshop on Intelligent Statistical Quality Control, Springer, 2019, pp. 265–286.
   Google Scholar
• C. Zou and P. Qiu, Multivariate statistical process control using lasso, J. Am. Stat. Assoc. 104 (2009), pp. 1586–1596.
   Web of Science ®Google Scholar
• C. Zou, F. Tsung, and Z. Wang, Monitoring profiles based on nonparametric regression methods, Technometrics 50 (2008), pp. 512–526.
   Web of Science ®Google Scholar