Clustering Then Estimation of Spatio-Temporal Self-Exciting Processes

Published Online:https://doi.org/10.1287/ijoc.2022.0351

References

  • Adikari S, Dutta K (2019) A new approach to real-time bidding in online advertisements: Auto pricing strategy. INFORMS J. Comput. 31(1):66–82.LinkGoogle Scholar
  • Ahn D, Shin D, Zeevi A (2023) Feature misspecification in sequential learning problems. Research paper, Columbia Business School, New York.Google Scholar
  • Balderama E, Schoenberg FP, Murray E, Rundel PW (2012) Application of branching models in the study of invasive species. J. Amer. Statist. Assoc. 107(498):467–476.CrossrefGoogle Scholar
  • Bichler M, Hammerl A, Morrill T, Waldherr S (2021) How to assign scarce resources without money: Designing information systems that are efficient, truthful, and (pretty) fair. Inform. Systems Res. 32(2):335–355.LinkGoogle Scholar
  • Birant D, Kut A (2007) ST-DBSCAN: An algorithm for clustering spatial–temporal data. Data Knowl. Eng. 60(1):208–221.CrossrefGoogle Scholar
  • Bollapragada R, Li Y, Rao US (2006) Budget-constrained, capacitated hub location to maximize expected demand coverage in fixed-wireless telecommunication networks. INFORMS J. Comput. 18(4):422–432.LinkGoogle Scholar
  • Brice P, Jiang W, Wan G (2011) A cluster-based context-tree model for multivariate data streams with applications to anomaly detection. INFORMS J. Comput. 23(3):364–376.LinkGoogle Scholar
  • Brown L, Gans N, Mandelbaum A, Sakov A, Shen H, Zeltyn S, Zhao L (2005) Statistical analysis of a telephone call center: A queueing-science perspective. J. Amer. Statist. Assoc. 100(469):36–50.CrossrefGoogle Scholar
  • Chen X (2021) Perfect sampling of Hawkes processes and queues with Hawkes arrivals. Stoch. Syst. 11(13):264–283.LinkGoogle Scholar
  • Chen N, Liu Y (2014) American option sensitivities estimation via a generalized infinitesimal perturbation analysis approach. Oper. Res. 62(3):616–632.LinkGoogle Scholar
  • Chen H, Schmeiser BW (2019) Mise-optimal intervals for MNO–PQRS estimators of Poisson rate functions. 2019 Winter Simulation Conf. (WSC) (IEEE, Piscataway, NJ), 368–379.Google Scholar
  • Chen S, Xie W (2022) On cluster-aware supervised learning: Frameworks, convergent algorithms, and applications. INFORMS J. Comput. 34(1):481–502.LinkGoogle Scholar
  • Chen N, Lee DK, Negahban SN (2019) Super-resolution estimation of cyclic arrival rates. Ann. Statist. 47(3):1754–1775.CrossrefGoogle Scholar
  • Chen N, Gürlek R, Lee DK, Shen H (2024) Can customer arrival rates be modelled by sine waves? Service Sci. 16(2):70–84.Google Scholar
  • Crane R, Sornette D (2008) Robust dynamic classes revealed by measuring the response function of a social system. Proc. Natl. Acad. Sci. USA 105(41):15649–15653.CrossrefGoogle Scholar
  • Cui T, Ouyang Y, Shen ZJM (2010) Reliable facility location design under the risk of disruptions. Oper. Res. 58(4-part-1):998–1011.Google Scholar
  • Daley DJ, Vere-Jones D (2003) An Introduction to the Theory of Point Processes: Volume I: Elementary Theory and Methods (Springer, New York), 211–275.Google Scholar
  • Daley DJ, Vere-Jones D (2007) An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure (Springer Science & Business Media, New York).Google Scholar
  • Daw A, Pender J (2018) Queues driven by Hawkes processes. Stoch. Syst. 8(3):192–229.LinkGoogle Scholar
  • Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J. Royal Statist. Soc. Series B (Methodological) 39(1):1–38.Google Scholar
  • Diggle PJ (2006) Spatio-temporal point processes: Methods and applications. Monogr. Statist. Appl. Probab. 107:1–46.Google Scholar
  • Dong Z, Zhu S, Xie Y, Mateu J, Rodríguez-Cortés FJ (2023) Non-stationary spatio-temporal point process modeling for high-resolution COVID-19 data. J. Royal Statist. Soc. Ser. C App. Statist. 72(2):368–386.Google Scholar
  • Du N, Farajtabar M, Ahmed A, Smola AJ, Song L (2015) Dirichlet-Hawkes processes with applications to clustering continuous-time document streams. Proc. 21st ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (ACM, New York), 219–228.Google Scholar
  • Du N, Dai H, Trivedi R, Upadhyay U, Gomez-Rodriguez M, Song L (2016) Recurrent marked temporal point processes: Embedding event history to vector. Proc. 22nd ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (ACM, New York), 1555–1564.Google Scholar
  • Errais E, Giesecke K, Goldberg LR (2010) Affine point processes and portfolio credit risk. SIAM J. Financial Math. 1(1):642–665.CrossrefGoogle Scholar
  • Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Second Internat. Conf. Knowledge Discovery Data Mining 96(34):226–231.Google Scholar
  • Fan S, Li X, Zhao JL (2017) Collaboration process pattern approach to improving teamwork performance: A data mining-based methodology. INFORMS J. Comput. 29(3):438–456.LinkGoogle Scholar
  • Farajtabar M, Wang Y, Gomez Rodriguez M, Li S, Zha H, Song L (2017) Coevolve: A joint point process model for information diffusion and network co-evolution. Cortes C, Lawrence N, Lee D, Sugiyama M, Garnett R, eds. Advances in Neural Information Processing Systems, vol. 28 (Curran Associates, Inc., Red Hook, NY).Google Scholar
  • Fierro R, Leiva V, Møller J (2015) The Hawkes process with different exciting functions and its asymptotic behavior. J. Appl. Probab. 52(1):37–54.CrossrefGoogle Scholar
  • Filimonov V, Sornette D (2012) Quantifying reflexivity in financial markets: Toward a prediction of flash crashes. Phys. Rev. E 85(5):056108.CrossrefGoogle Scholar
  • Fuentes-Santos I, Gonzaléz-Manteiga W, Zubelli J (2021) Nonparametric spatiotemporal analysis of violent crime. A case study in the Rio de Janeiro metropolitan area. Spat. Stat. 42:100431.CrossrefGoogle Scholar
  • Gan G, Ma C, Wu J (2020) Data Clustering: Theory, Algorithms, and Applications (Society for Industrial and Applied Mathematics, Philadelphia).Google Scholar
  • Gao X, Zhu L (2018) Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues. Queueing Syst. 90:161–206.CrossrefGoogle Scholar
  • Gopal RD, Ramesh R (1995) The query clustering problem: A set partitioning approach. IEEE Trans. Knowledge Data Eng. 7(6):885–899.CrossrefGoogle Scholar
  • Guo Z, Li J, Ramesh R (2019) Optimal management of virtual infrastructures under flexible cloud service agreements. Inform. Systems Res. 30(4):1424–1446.LinkGoogle Scholar
  • Guo Z, Li J, Ramesh R (2020) Scalable, adaptable, and fast estimation of transient downtime in virtual infrastructures using convex decomposition and sample path randomization. INFORMS J. Comput. 32(2):321–345.AbstractGoogle Scholar
  • Hawkes AG (1971) Spectra of some self-exciting and mutually exciting point processes. Biometrika 58(1):83–90.CrossrefGoogle Scholar
  • Hawkes AG, Oakes D (1974) A cluster process representation of a self-exciting process. J. Appl. Probab. 11(3):493–503.CrossrefGoogle Scholar
  • Henderson SG (2003) Estimation for nonhomogeneous Poisson processes from aggregated data. Oper. Res. Lett. 31(5):375–382.CrossrefGoogle Scholar
  • Hu J, Reiter JP, Wang Q (2018) Dirichlet process mixture models for modeling and generating synthetic versions of nested categorical data. Bayesian Anal. 13(1):183–200.CrossrefGoogle Scholar
  • Jian N, Henderson SG (2015) An introduction to simulation optimization. 2015 Winter Simulation Conf. (WSC) (IEEE, Piscataway, NJ), 1780–1794.Google Scholar
  • Jolliffe IT, Cadima J (2016) Principal component analysis: A review and recent developments. Philos. Trans. Roy. Soc. A 374(2065):20150202.CrossrefGoogle Scholar
  • Kim SH, Whitt W (2014a) Are call center and hospital arrivals well modeled by nonhomogeneous Poisson processes? Manufacturing Service Oper. Management 16(3):464–480.LinkGoogle Scholar
  • Kim SH, Whitt W (2014b) Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process. Naval Res. Logist. 61(1):66–90.CrossrefGoogle Scholar
  • Kohonen T (1990) The self-organizing map. Proc. IEEE 78(9):1464–1480.CrossrefGoogle Scholar
  • Kuhl ME, Wilson JR (2001) Modeling and simulating Poisson processes having trends or nontrigonometric cyclic effects. European J. Oper. Res. 133(3):566–582.CrossrefGoogle Scholar
  • Lee S, Wilson JR, Crawford MM (1991) Modeling and simulation of a nonhomogeneous Poisson process having cyclic behavior. Comm. Statist. Simulation Comput. 20(2–3):777–809.CrossrefGoogle Scholar
  • Li H, Li H, Bhowmick SS (2020) Brunch: Branching structure inference of hybrid multivariate Hawkes processes with application to social media. Adv. Knowledge Discovery Data Mining: 24th Pacific-Asia Conf., PAKDD 2020, Proc., vol. 24, Part I (Springer International Publishing, New York), 553–566.Google Scholar
  • Li C, Song Z, Wang X (2019) Nonparametric method for modeling clustering phenomena in emergency calls under spatial-temporal self-exciting point processes. IEEE Access 7:24865–24876.CrossrefGoogle Scholar
  • Li J, Liu C, Yu JX, Chen Y, Sellis T, Culpepper JS (2016) Personalized influential topic search via social network summarization. IEEE Trans. Knowledge Data Eng. 28(7):1820–1834.CrossrefGoogle Scholar
  • Li S, Xiao S, Zhu S, Du N, Xie Y, Song L (2018) Learning temporal point processes via reinforcement learning. Proc. 32nd Internat. Conf. Neural Inform. Processing Systems (Curran Associates Inc., Red Hook, NY), 10804–10814.Google Scholar
  • Lima R (2023) Hawkes processes modeling, inference, and control: An overview. SIAM Rev. 65(2):331–374.CrossrefGoogle Scholar
  • Lin SB, Tang S, Wang Y, Wang D (2022) Toward efficient ensemble learning with structure constraints: Convergent algorithms and applications. INFORMS J. Comput. 34(6):3096–3116.Google Scholar
  • Liu Y, Shi J, Chen Y (2019b) Thread structure learning on online health forums with partially labeled data. IEEE Trans. Comput. Soc. Syst. 6(6):1273–1282.CrossrefGoogle Scholar
  • Liu Y, Yan T, Chen H (2018) Exploiting graph regularized multi-dimensional Hawkes processes for modeling events with spatio-temporal characteristics. IJCAI (AAAI Press, Palo Alto, CA), 2475–2482.Google Scholar
  • Liu R, Kuhl ME, Liu Y, Wilson JR (2019a) Modeling and simulation of nonstationary non-Poisson arrival processes. INFORMS J. Comput. 31(2):347–366.LinkGoogle Scholar
  • Manrique-Vallier D, Hu J (2018) Bayesian non-parametric generation of fully synthetic multivariate categorical data in the presence of structural zeros. J. Roy. Statist. Soc. Ser. A 181(3):635–647.CrossrefGoogle Scholar
  • Mehrdad B, Zhu L (2014) On the Hawkes process with different exciting functions. Preprint, submitted March 5, https://arxiv.org/abs/1403.0994.Google Scholar
  • Mei H, Eisner J (2017) The neural Hawkes process: A neurally self-modulating multivariate point process. Proc. 31st Internat. Conf. Neural Inform. Processing Systems (Curran Associates Inc., Red Hook, NY), 6757–6767.Google Scholar
  • Meng Q, Xiao K, Shen D, Zhu H, Xiong H (2022) Fine-grained job salary benchmarking with a nonparametric Dirichlet process–based latent factor model. INFORMS J. Comput. 34(5):2443–2463.LinkGoogle Scholar
  • Mohler G (2014) Marked point process hotspot maps for homicide and gun crime prediction in Chicago. Internat. J. Forecast. 30(3):491–497.CrossrefGoogle Scholar
  • Mohler GO, Short MB, Brantingham PJ, Schoenberg FP, Tita GE (2011) Self-exciting point process modeling of crime. J. Amer. Statist. Assoc. 106(493):100–108.CrossrefGoogle Scholar
  • Morgan LE, Nelson BL, Titman AC, Worthington DJ (2019) A spline-based method for modelling and generating a nonhomogeneous Poisson process. 2019 Winter Simulation Conf. (WSC) (IEEE, Piscataway, NJ), 356–367.Google Scholar
  • Nelson BL, Leemis LM (2020) The ease of fitting but futility of testing a nonstationary Poisson processes from one sample path. 2020 Winter Simulation Conf. (WSC) (IEEE, Piscataway, NJ), 266–276.Google Scholar
  • Nielsen F (2016) Hierarchical Clustering. Introduction to HPC with MPI for Data Science (Springer, New York), 195–211.CrossrefGoogle Scholar
  • Ogata Y (1998) Space-time point-process models for earthquake occurrences. Ann. Inst. Statist. Math. 50(2):379–402.CrossrefGoogle Scholar
  • Ozaki T (1979) Maximum likelihood estimation of Hawkes’ self-exciting point processes. Ann. Inst. Statist. Math. 31(1):145–155.CrossrefGoogle Scholar
  • Pasupathy R (2010) Generating Homogeneous Poisson Processes, Wiley Encyclopedia of Operations Research and Management Science (John Wiley, Hoboken, NJ).Google Scholar
  • Rathbun SL (1996) Asymptotic properties of the maximum likelihood estimator for spatio-temporal point processes. J. Statist. Plann. Inference 51(1):55–74.CrossrefGoogle Scholar
  • Reinhart A (2018) A review of self-exciting spatio-temporal point processes and their applications. Statist. Sci. 33(3):299–318.Google Scholar
  • Resnick SI (1992) Adventures in Stochastic Processes (Birkhäuser, Boston).Google Scholar
  • Rizoiu MA, Lee Y, Mishra S, Xie L (2017) Hawkes processes for events in social media. Frontiers of Multimedia Research (Association for Computing Machinery and Morgan & Claypool, New York), 191–218.Google Scholar
  • Saltzman EA, Drew JH, Leemis LM, Henderson SG (2012) Simulating multivariate nonhomogeneous Poisson processes using projections. ACM Trans. Model. Comput. Simul. 22(3):1–13.CrossrefGoogle Scholar
  • Schoenberg FP (2005) Consistent parametric estimation of the intensity of a spatial-temporal point process. J. Statist. Plann. Inference 128(1):79–93.CrossrefGoogle Scholar
  • Schubert E, Sander J, Ester M, Kriegel HP, Xu X (2017) DBSCAN revisited, revisited: Why and how you should (still) use DBSCAN. ACM Trans. Database Syst. 42(3):1–21.CrossrefGoogle Scholar
  • Seref O, Fan YJ, Chaovalitwongse WA (2014) Mathematical programming formulations and algorithms for discrete k-median clustering of time-series data. INFORMS J. Comput. 26(1):160–172.LinkGoogle Scholar
  • Tari L, Tu PH, Hakenberg J, Chen Y, Son TC, Gonzalez G, Baral C (2010) Incremental information extraction using relational databases. IEEE Trans. Knowledge Data Eng. 24(1):86–99.CrossrefGoogle Scholar
  • Ungun B, Xing L, Boyd S (2019) Real-time radiation treatment planning with optimality guarantees via cluster and bound methods. INFORMS J. Comput. 31(3):544–558.LinkGoogle Scholar
  • Veen A, Schoenberg FP (2008) Estimation of space–time branching process models in seismology using an EM–type algorithm. J. Amer. Statist. Assoc. 103(482):614–624.CrossrefGoogle Scholar
  • Wang S, Ng SH, Haskell WB (2022) A multilevel simulation optimization approach for quantile functions. INFORMS J. Comput. 34(1):569–585.LinkGoogle Scholar
  • Xiao S, Yan J, Yang X, Zha H, Chu S (2017b) Modeling the intensity function of point process via recurrent neural networks. Proc. AAAI Conf. Artificial Intelligence 31(1).Google Scholar
  • Xiao S, Farajtabar M, Ye X, Yan J, Song L, Zha H (2017a) Wasserstein learning of deep generative point process models. Proc. 31st Internat. Conf. Neural Inform. Processing Systems (Curran Associates Inc., Red Hook, NY), 3250–3259.Google Scholar
  • Xiao S, Xu H, Yan J, Farajtabar M, Yang X, Song L, Zha H (2018) Learning conditional generative models for temporal point processes. Proc. AAAI Conf. Artificial Intelligence (AAAI Press, Palo Alto, CA), vol. 32.Google Scholar
  • Xu H, Zha H (2017) A Dirichlet mixture model of Hawkes processes for event sequence clustering. Guyon I, Von Luxburg U, Bengio S, Wallach H, Fergus R, Vishwanathan S, Garnett R, eds. Advances in Neural Information Processing Systems, vol. 30 (Curran Associates Inc., Red Hook, NY).Google Scholar
  • Yamin K, Wang H, Montreuil B, Xie Y (2022) Online detection of supply chain network disruptions using sequential change-point detection for Hawkes processes. Preprint, submitted November 22, https://arxiv.org/abs/2211.12091.Google Scholar
  • Yang SH, Zha H (2013) Mixture of mutually exciting processes for viral diffusion. Internat. Conf. Machine Learn. (PMLR, New York), 1–9.Google Scholar
  • Yuan B, Li H, Bertozzi AL, Brantingham PJ, Porter MA (2019) Multivariate spatiotemporal Hawkes processes and network reconstruction. SIAM J. Math. Data Sci. 1(2):356–382.CrossrefGoogle Scholar
  • Zhang K, Shasha D (1989) Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18(6):1245–1262.CrossrefGoogle Scholar
  • Zhang H, Zheng Z (2020) Simulating nonstationary spatio-temporal Poisson processes using the inversion method. 2020 Winter Simulation Conf. (WSC) (IEEE, Piscataway, NJ), 492–503.Google Scholar
  • Zhang X, Hong LJ, Zhang J (2014) Scaling and modeling of call center arrivals. Proc. Winter Simulation Conf. 2014 (IEEE, Piscataway, NJ), 476–485.Google Scholar
  • Zhang H, Zhan D, Anderson J, Righter R, Zheng Z (2024) Clustering then estimation of spatio-temporal self-exciting processes. Accessed June 29, 2024, https://github.com/INFORMSJoC/2022.0351.Google Scholar
  • Zheng Z, Glynn PW (2017) Fitting continuous piecewise linear Poisson intensities via maximum likelihood and least squares. 2017 Winter Simulation Conference (WSC) (IEEE, Piscataway, NJ), 1740–1749.Google Scholar
  • Zhou K, Zha H, Song L (2013a) Learning Social Infectivity in Sparse Low-Rank Networks Using Multi-Dimensional Hawkes Processes. Artificial Intelligence and Statistics (PMLR, New York), 641–649.Google Scholar
  • Zhou K, Zha H, Song L (2013b) Learning triggering kernels for multi-dimensional Hawkes processes. Internat. Conf. Machine Learn. (PMLR, New York), 1301–1309.Google Scholar
  • Zhou Z, Matteson DS, Woodard DB, Henderson SG, Micheas AC (2015) A spatio-temporal point process model for ambulance demand. J. Amer. Statist. Assoc. 110(509):6–15.CrossrefGoogle Scholar
  • Zhu S, Xie Y (2022) Spatiotemporal-textual point processes for crime linkage detection. Ann. Appl. Stat. 16(2):1151–1170.CrossrefGoogle Scholar
  • Zhu S, Li S, Peng Z, Xie Y (2021a) Imitation learning of neural spatio-temporal point processes. IEEE Trans. Knowledge Data Eng. 34(11):5391–5402.Google Scholar
  • Zhu S, Ding R, Zhang M, Van Hentenryck P, Xie Y (2020) Spatio-temporal point processes with attention for traffic congestion event modeling. Preprint, submitted May 15, https://arxiv.org/abs/2005.08665.Google Scholar
  • Zhu S, Yao R, Xie Y, Qiu F, Wu X (2021b) Quantifying grid resilience against extreme weather using large-scale customer power outage data. Preprint, submitted September 20, https://arxiv.org/abs/2109.09711.Google Scholar
  • Zhuang J, Ogata Y, Vere-Jones D (2002) Stochastic declustering of space-time earthquake occurrences. J. Amer. Statist. Assoc. 97(458):369–380.CrossrefGoogle Scholar
  • Zhuang J, Ogata Y, Vere-Jones D (2004) Analyzing earthquake clustering features by using stochastic reconstruction. J. Geophys. Res. Solid Earth 109(B5):1–17.CrossrefGoogle Scholar
  • Zipkin JR, Schoenberg FP, Coronges K, Bertozzi AL (2016) Point-process models of social network interactions: Parameter estimation and missing data recovery. Eur. J. Appl. Math. 27(3):502–529.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.