Sequential Change-Point Detection for Mutually Exciting Point Processes

References

• Achab, M., Bacry, E., Gaïffas, S., Mastromatteo, I., and Muzy, J.-F. (2017), “Uncovering Causality from Multivariate Hawkes Integrated Cumulants,” The Journal of Machine Learning Research, 18, 6998–7025.
   Web of Science ®Google Scholar
• Brette, R., and Gerstner, W. (2005), “Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity,” Journal of Neurophysiology, 94, 3637–3642. DOI: 10.1152/jn.00686.2005.
   PubMed Web of Science ®Google Scholar
• Chiang, W.-H., Liu, X., and Mohler, G. (2021), “Hawkes Process Modeling of Covid-19 with Mobility Leading Indicators and Spatial Covariates,” International Journal of Forecasting, 38, 505–520. DOI: 10.1016/j.ijforecast.2021.07.001.
   PubMed Web of Science ®Google Scholar
• Daley, D. J., and Vere-Jones, D. (2003), An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods, New York: Springer.
   Google Scholar
• Eliasmith, C., and Anderson, C. H. (2003), Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems, Cambridge, MA: MIT Press.
   Google Scholar
• Goense, J., and Ratnam, R. (2003), “Continuous Detection of Weak Sensory Signals in Afferent Spike Trains: The Role of Anti-correlated Interspike Intervals in Detection Performance,” Journal of Comparative Physiology A, 189, 741–759. DOI: 10.1007/s00359-003-0449-4.
   Web of Science ®Google Scholar
• Hawkes, A. G. (1971), “Spectra of Some Self-exciting and Mutually Exciting Point Processes,” Biometrika, 58, 83–90. DOI: 10.1093/biomet/58.1.83.
   Web of Science ®Google Scholar
• Hawkes, A. G. (2018), “Hawkes Processes and their Applications to Finance: A Review,” Quantitative Finance, 18, 193–198. DOI: 10.1080/14697688.2017.1403131.
   Web of Science ®Google Scholar
• Lambert, R. C., Tuleau-Malot, C., Bessaih, T., Rivoirard, V., Bouret, Y., Leresche, N., and Reynaud-Bouret, P. (2018), ‘Reconstructing the Functional Connectivity of Multiple Spike Trains Using Hawkes Models,” Journal of Neuroscience Methods, 297, 9–21. DOI: 10.1016/j.jneumeth.2017.12.026.
   PubMed Web of Science ®Google Scholar
• Li, S., Xie, Y., Farajtabar, M., Verma, A., and Song, L. (2017), “Detecting Changes in Dynamic Events Over Networks,” IEEE Transactions on Signal and Information Processing over Networks, 3, 346–359. DOI: 10.1109/TSIPN.2017.2696264.
   Web of Science ®Google Scholar
• Lorden, G. (1971), “Procedures for Reacting to a Change in Distribution,” Annals of Mathematical Statistics, 42, 1897–1908. DOI: 10.1214/aoms/1177693055.
   Google Scholar
• Mohler, G. O., Short, M. B., Brantingham, P. J., Schoenberg, F. P., and Tita, G. E. (2011), “Self-exciting Point Process Modeling of Crime,” Journal of the American Statistical Association, 106, 100–108. DOI: 10.1198/jasa.2011.ap09546.
   Web of Science ®Google Scholar
• Ogata, Y. (1978), “The Asymptotic Behaviour of Maximum Likelihood Estimators for Stationary Point Processes,” Annals of the Institute of Statistical Mathematics, 30, 243–261. DOI: 10.1007/BF02480216.
   Web of Science ®Google Scholar
• Ogata, Y. (1988), “Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes,” Journal of the American Statistical Association, 83, 9–27.
   Web of Science ®Google Scholar
• Ogata, Y. (1998), “Space-time Point-process Models for Earthquake Occurrences,” Annals of the Institute of Statistical Mathematics, 50, 379–402.
   Web of Science ®Google Scholar
• Page, E. S. (1954), “Continuous Inspection Schemes,” Biometrika, 41, 100–115.
   Web of Science ®Google Scholar
• Pollak, M. (1985), “Optimal Detection of a Change in Distribution,” Annals of Statistics, 13, 206–227.
   Web of Science ®Google Scholar
• Rambaldi, M., Filimonov, V., and Lillo, F. (2018), “Detection of Intensity Bursts Using Hawkes Processes: An Application to High-Frequency Financial Data,” Physical Review E, 97, 032318. DOI: 10.1103/PhysRevE.97.032318.
   PubMed Web of Science ®Google Scholar
• Rasmussen, J. G. (2011), “Temporal Point Processes: The Conditional Intensity Function,” Lecture Notes, Jan.
   Google Scholar
• Reinhart, A. (2018), “A Review of Self-exciting Spatio-Temporal Point Processes and their Applications,” Statistical Science, 33, 299–318.
   Web of Science ®Google Scholar
• Reynaud-Bouret, P., Rivoirard, V., and Tuleau-Malot, C. (2013), “Inference of Functional Connectivity in Neurosciences via Hawkes Processes,” in IEEE Global Conference on Signal and Information Processing, pp. 317–320. IEEE.
   Google Scholar
• Reynaud-Bouret, P., and Roy, E. (2007), “Some Non asymptotic Tail Estimates for Hawkes Processes,” Bulletin of the Belgian Mathematical Society-Simon Stevin, 13, 883–896.
   Web of Science ®Google Scholar
• Rizoiu, M.-A., Mishra, S., Kong, Q., Carman, M., and Xie, L. (2018), “SIR-Hawkes: Linking Epidemic Models and Hawkes Processes to Model Diffusions in Finite Populations,” in Proceedings of the 2018 World Wide Web Conference, pp. 419–428.
   Google Scholar
• Shewhart, W. A. (1925), “The Application of Statistics as an Aid in Maintaining Quality of a Manufactured Product,” Journal of the American Statistical Association, 20, 546–548. DOI: 10.1080/01621459.1925.10502930.
   Google Scholar
• Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, Milwaukee, WI: American Society for Quality Control.
   Google Scholar
• Tang, S., Zhang, Y., Li, Z., Li, M., Liu, F., Jiang, H., and Lee, T. S. (2018), “Large-Scale Two-Photon Imaging Revealed Super-Sparse Population Codes in the V1 Superficial Layer of Awake Monkeys,” Elife, 7, e33370. DOI: 10.7554/eLife.33370.
   PubMed Web of Science ®Google Scholar
• Tartakovsky, A., Nikiforov, I., and Basseville, M. (2015), Sequential Analysis: Hypothesis Testing and Changepoint Detection. ser. Monographs on Statistics and Applied Probability 136. Boca Raton, FL: Chapman and Hall/CRC Press.
   Google Scholar
• Tartakovsky, A. G. (2020), Sequential Change Detection and Hypothesis Testing: General Non-iid Stochastic Models and Asymptotically Optimal Rules. ser. Monographs on Statistics and Applied Probability 165. Boca Raton, FL: Chapman and Hall/CRC Press.
   Google Scholar
• Wang, D., Yu, Y., and Willett, R. (2020a), “Detecting Abrupt Changes in High-Dimensional Self-exciting Poisson Processes,” arXiv preprint arXiv:2006.03572.
   Google Scholar
• Wang, H., Xie, L., Cuozzo, A., Mak, S., and Xie, Y. (2020b), “Uncertainty Quantification for Inferring Hawkes Networks,” in Advances in Neural Information Processing Systems, 33.
   Google Scholar
• Xie, L., Xie, Y., and Moustakides, G. V. (2020), “Sequential Subspace Change Point Detection,” Sequential Analysis, 39, 307–335. DOI: 10.1080/07474946.2020.1823191.
   Web of Science ®Google Scholar
• Xie, L., Zou, S., Xie, Y., and Veeravalli., V. V. (2021), “Sequential Change Detection: Classical Results and New Directions,” IEEE Journal on Selected Areas in Information Theory, 2, 494–514. DOI: 10.1109/JSAIT.2021.3072962.
   Google Scholar
• Xie, Y., and Siegmund, D. (2012), “Spectrum Opportunity Detection with Weak and Correlated Signals,” in Conference Record of the Forty Sixth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), pp. 128–132. IEEE.
   Google Scholar
• Yang, S.-H., and Zha, H. (2013), Mixture of Mutually Exciting Processes for Viral Diffusion,” in International Conference on Machine Learning, pp. 1–9. PMLR.
   Google Scholar
• Zhou, F., Li, Z., Fan, X., Wang, Y., Sowmya, A., and Chen, F. (2020), “Fast Multi-Resolution Segmentation for Nonstationary Hawkes Process Using Cumulants,” International Journal of Data Science and Analytics, 10, 321–330. DOI: 10.1007/s41060-020-00223-3.
   Google Scholar