Simulation and Calibration of a Fully Bayesian Marked Multidimensional Hawkes Process with Dissimilar Decays

Kar Wai Lim, Young Lee, Leif Hanlen, Hongbiao Zhao
Proceedings of The 8th Asian Conference on Machine Learning, PMLR 63:238-253, 2016.

Abstract

We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler auxiliary variables that can be sampled directly, giving exact simulation with no approximation. We establish that the auxiliary variables provides information on the parent process for each event time. The algorithm correctness is shown by verifying the simulated intensities with their theoretical moments. A modular inference procedure consisting of a combination between Gibbs through the adaptive rejection sampling and Metropolis Hastings steps is presented. Finally, we compare our proposed simulation method against existing methods, and find significant improvement in terms of algorithm speed. Our inference algorithm is used to discover the strengths of mutually excitations in real dark networks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v63-lim83, title = {Simulation and Calibration of a Fully Bayesian Marked Multidimensional Hawkes Process with Dissimilar Decays}, author = {Lim, Kar Wai and Lee, Young and Hanlen, Leif and Zhao, Hongbiao}, booktitle = {Proceedings of The 8th Asian Conference on Machine Learning}, pages = {238--253}, year = {2016}, editor = {Durrant, Robert J. and Kim, Kee-Eung}, volume = {63}, series = {Proceedings of Machine Learning Research}, address = {The University of Waikato, Hamilton, New Zealand}, month = {16--18 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v63/lim83.pdf}, url = {https://proceedings.mlr.press/v63/lim83.html}, abstract = {We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler auxiliary variables that can be sampled directly, giving exact simulation with no approximation. We establish that the auxiliary variables provides information on the parent process for each event time. The algorithm correctness is shown by verifying the simulated intensities with their theoretical moments. A modular inference procedure consisting of a combination between Gibbs through the adaptive rejection sampling and Metropolis Hastings steps is presented. Finally, we compare our proposed simulation method against existing methods, and find significant improvement in terms of algorithm speed. Our inference algorithm is used to discover the strengths of mutually excitations in real dark networks. } }
Endnote
%0 Conference Paper %T Simulation and Calibration of a Fully Bayesian Marked Multidimensional Hawkes Process with Dissimilar Decays %A Kar Wai Lim %A Young Lee %A Leif Hanlen %A Hongbiao Zhao %B Proceedings of The 8th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Robert J. Durrant %E Kee-Eung Kim %F pmlr-v63-lim83 %I PMLR %P 238--253 %U https://proceedings.mlr.press/v63/lim83.html %V 63 %X We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler auxiliary variables that can be sampled directly, giving exact simulation with no approximation. We establish that the auxiliary variables provides information on the parent process for each event time. The algorithm correctness is shown by verifying the simulated intensities with their theoretical moments. A modular inference procedure consisting of a combination between Gibbs through the adaptive rejection sampling and Metropolis Hastings steps is presented. Finally, we compare our proposed simulation method against existing methods, and find significant improvement in terms of algorithm speed. Our inference algorithm is used to discover the strengths of mutually excitations in real dark networks.
RIS
TY - CPAPER TI - Simulation and Calibration of a Fully Bayesian Marked Multidimensional Hawkes Process with Dissimilar Decays AU - Kar Wai Lim AU - Young Lee AU - Leif Hanlen AU - Hongbiao Zhao BT - Proceedings of The 8th Asian Conference on Machine Learning DA - 2016/11/20 ED - Robert J. Durrant ED - Kee-Eung Kim ID - pmlr-v63-lim83 PB - PMLR DP - Proceedings of Machine Learning Research VL - 63 SP - 238 EP - 253 L1 - http://proceedings.mlr.press/v63/lim83.pdf UR - https://proceedings.mlr.press/v63/lim83.html AB - We propose a simulation method for multidimensional Hawkes processes based on superposition theory of point processes. This formulation allows us to design efficient simulations for Hawkes processes with differing exponentially decaying intensities. We demonstrate that inter-arrival times can be decomposed into simpler auxiliary variables that can be sampled directly, giving exact simulation with no approximation. We establish that the auxiliary variables provides information on the parent process for each event time. The algorithm correctness is shown by verifying the simulated intensities with their theoretical moments. A modular inference procedure consisting of a combination between Gibbs through the adaptive rejection sampling and Metropolis Hastings steps is presented. Finally, we compare our proposed simulation method against existing methods, and find significant improvement in terms of algorithm speed. Our inference algorithm is used to discover the strengths of mutually excitations in real dark networks. ER -
APA
Lim, K.W., Lee, Y., Hanlen, L. & Zhao, H.. (2016). Simulation and Calibration of a Fully Bayesian Marked Multidimensional Hawkes Process with Dissimilar Decays. Proceedings of The 8th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 63:238-253 Available from https://proceedings.mlr.press/v63/lim83.html.

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