Hawkes Processes with Stochastic Excitations. Lee, Y., Lim, K. W., & Ong, C. S. In Balcan, M. F. & Weinberger, K. Q., editors, Proceedings of The 33rd International Conference on Machine Learning, volume 48, of Proceedings of Machine Learning Research, pages 79--88, New York, New York, USA, 20--22 Jun, 2016. PMLR. ![Hawkes Processes with Stochastic Excitations [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.
@inproceedings{pmlr-v48-leea16,
Abstract = {We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.},
Address = {New York, New York, USA},
Author = {Young Lee and Kar Wai Lim and Cheng Soon Ong},
Booktitle = {Proceedings of The 33rd International Conference on Machine Learning},
Date-Modified = {2017-09-27 08:52:57 +0000},
Editor = {Maria Florina Balcan and Kilian Q. Weinberger},
Keywords = {machine learning},
Month = {20--22 Jun},
Pages = {79--88},
Pdf = {http://proceedings.mlr.press/v48/leea16.pdf},
Publisher = {PMLR},
Series = {Proceedings of Machine Learning Research},
Title = {Hawkes Processes with Stochastic Excitations},
Url = {http://proceedings.mlr.press/v48/leea16.html},
Volume = {48},
Year = {2016},
Bdsk-Url-1 = {http://proceedings.mlr.press/v48/leea16.html}}
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