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A Refined MISD Algorithm Based on Gaussian Process Regression

Part of the Lecture Notes in Computer Science book series (LNAI,volume 10938)

Abstract

Time series data is a common data type in real life, and modelling of time series data along with its underlying temporal dynamics is always a challenging job. Temporal point process is an outstanding method to model time series data in domains that require temporal continuity, and includes homogeneous Poisson process, inhomogeneous Poisson process and Hawkes process. We focus on Hawkes process which can explain self-exciting phenomena in many real applications. In classical Hawkes process, the triggering kernel is always assumed to be an exponential decay function, which is inappropriate for some scenarios, so nonparametric methods have been used to deal with this problem, such as model independent stochastic de-clustering (MISD) algorithm. However, MISD algorithm has a strong dependence on the number of bins, which leads to underfitting for some bins and overfitting for others, so the choice of bin number is a critical step. In this paper, we innovatively embed a Gaussian process regression into the iterations of MISD to make this algorithm less sensitive to the choice of bin number.

Keywords

  • Hawkes process
  • MISD
  • Gaussian process
  • Nonparametric

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Notes

  1. 1.

    We assume all the bins are equally wide.

  2. 2.

    https://data.cityofnewyork.us/Public-Safety/NYPD-Motor-Vehicle-Collisions/h9gi-nx95.

  3. 3.

    https://data.cityofnewyork.us/Public-Safety/NYPD-Complaint-Data-Current-YTD/5uac-w243.

References

  1. Mikolov, T., Karafit, M., Burget, L., Cernock, J., Khudanpur, S.: Recurrent neural network based language model. In: Interspeech, vol. 2, p. 3 (2010)

    Google Scholar 

  2. Schoenberg, F.P., Brillinger, D.R., Guttorp, P.: Point processes, spatialtemporal. In: Encyclopedia of Environmetrics (2002)

    Google Scholar 

  3. Thompson Jr., W.A.: Homogeneous Poisson processes. In: Point Process Models with Applications to Safety and Reliability, pp. 21–31. Springer, Boston (1988). https://doi.org/10.1007/978-1-4613-1067-9_3

    CrossRef  Google Scholar 

  4. Weinberg, J., Brown, L.D., Stroud, J.R.: Bayesian forecasting of an inhomogeneous Poisson process with applications to call center data. J. Am. Stat. Assoc. 102(480), 1185–1198 (2007)

    MathSciNet  CrossRef  Google Scholar 

  5. Hawkes, A.G.: Spectra of some self-exciting and mutually exciting point processes. Biometrika 58(1), 83–90 (1971)

    MathSciNet  CrossRef  Google Scholar 

  6. Vere-Jones, D.: Stochastic models for earthquake occurrence. J. Roy. Stat. Soc. Ser. B (Methodological) 32, 1–62 (1970)

    MathSciNet  MATH  Google Scholar 

  7. Short, M.B., Mohler, G.O., Brantingham, P.J., Tita, G.E.: Gang rivalry dynamics via coupled point process networks. Discret. Contin. Dyn. Syst. Ser. B 19(5), 1459–1477 (2014)

    MathSciNet  CrossRef  Google Scholar 

  8. Mitchell, L., Cates, M.E.: Hawkes process as a model of social interactions: a view on video dynamics. J. Phys. Math. Theor. 43(4), 045101 (2009)

    MathSciNet  CrossRef  Google Scholar 

  9. Mohler, G.O., Short, M.B., Brantingham, P.J., Schoenberg, F.P., Tita, G.E.: Self-exciting point process modeling of crime. J. Am. Stat. Assoc. 106(493), 100–108 (2011)

    MathSciNet  CrossRef  Google Scholar 

  10. Lewis, E., Mohler, G., Brantingham, P.J., Bertozzi, A.L.: Self-exciting point process models of civilian deaths in Iraq. Secur. J. 25(3), 244–264 (2012)

    CrossRef  Google Scholar 

  11. Marsan, D., Lengline, O.: Extending earthquakes reach through cascading. Science 319(5866), 1076–1079 (2008)

    CrossRef  Google Scholar 

  12. Ogata, Y.: Space-time point-process models for earthquake occurrences. Ann. Inst. Stat. Math. 50(2), 379–402 (1998)

    CrossRef  Google Scholar 

  13. Bacry, E., Jaisson, T., Muzy, J.F.: Estimation of slowly decreasing Hawkes kernels: application to high-frequency order book dynamics. Quant. Financ. 16(8), 1179–1201 (2016)

    MathSciNet  CrossRef  Google Scholar 

  14. Hardiman, S., Bercot, N., Bouchaud, J.P.: Critical reflexivity in financial markets: a Hawkes process analysis. Eur. Phys. J. B 86, 442 (2013)

    CrossRef  Google Scholar 

  15. Zhou, K., Zha, H., Song, L.: Learning social infectivity in sparse low-rank networks using multi-dimensional Hawkes processes. In: Artificial Intelligence and Statistics, pp. 641–649 (2013)

    Google Scholar 

  16. Zhou, K., Zha, H., Song, L.: Learning triggering kernels for multi-dimensional Hawkes processes. In: Proceedings of the 30th International Conference on Machine Learning, pp. 1301–1309 (2013)

    Google Scholar 

  17. Du, N., Song, L., Yuan, M., Smola, A.J.: Learning networks of heterogeneous influence. In: Advances in Neural Information Processing Systems, pp. 2780–2788 (2012)

    Google Scholar 

  18. Du, N., Dai, H., Trivedi, R., Upadhyay, U., Gomez-Rodriguez, M., Song, L.: Recurrent marked temporal point processes: embedding event history to vector. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 1555–1564 (2016)

    Google Scholar 

  19. Lewis, E., Mohler, G.: A nonparametric EM algorithm for multiscale Hawkes processes. J. Nonparametric Stat. 1(1), 1–20 (2011)

    Google Scholar 

  20. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)

    MATH  Google Scholar 

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Zhou, F., Li, Z., Fan, X., Wang, Y., Sowmya, A., Chen, F. (2018). A Refined MISD Algorithm Based on Gaussian Process Regression. In: Phung, D., Tseng, V., Webb, G., Ho, B., Ganji, M., Rashidi, L. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2018. Lecture Notes in Computer Science(), vol 10938. Springer, Cham. https://doi.org/10.1007/978-3-319-93037-4_46

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  • DOI: https://doi.org/10.1007/978-3-319-93037-4_46

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