Hawkes Processes with Stochastic Excitations

Young Lee, Kar Wai Lim, Cheng Soon Ong
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:79-88, 2016.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-leea16, title = {Hawkes Processes with Stochastic Excitations}, author = {Lee, Young and Lim, Kar Wai and Ong, Cheng Soon}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {79--88}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/leea16.pdf}, url = {https://proceedings.mlr.press/v48/leea16.html}, 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.} }
Endnote
%0 Conference Paper %T Hawkes Processes with Stochastic Excitations %A Young Lee %A Kar Wai Lim %A Cheng Soon Ong %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-leea16 %I PMLR %P 79--88 %U https://proceedings.mlr.press/v48/leea16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Hawkes Processes with Stochastic Excitations AU - Young Lee AU - Kar Wai Lim AU - Cheng Soon Ong BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-leea16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 79 EP - 88 L1 - http://proceedings.mlr.press/v48/leea16.pdf UR - https://proceedings.mlr.press/v48/leea16.html AB - 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. ER -
APA
Lee, Y., Lim, K.W. & Ong, C.S.. (2016). Hawkes Processes with Stochastic Excitations. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:79-88 Available from https://proceedings.mlr.press/v48/leea16.html.

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