Isotonic Hawkes Processes

Yichen Wang, Bo Xie, Nan Du, Le Song
; Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:2226-2234, 2016.

Abstract

Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications.

Cite this Paper


BibTeX
@InProceedings{pmlr-v48-wangg16, title = {Isotonic Hawkes Processes}, author = {Yichen Wang and Bo Xie and Nan Du and Le Song}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {2226--2234}, year = {2016}, editor = {Maria Florina Balcan and Kilian Q. Weinberger}, 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/wangg16.pdf}, url = {http://proceedings.mlr.press/v48/wangg16.html}, abstract = {Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications.} }
Endnote
%0 Conference Paper %T Isotonic Hawkes Processes %A Yichen Wang %A Bo Xie %A Nan Du %A Le Song %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-wangg16 %I PMLR %J Proceedings of Machine Learning Research %P 2226--2234 %U http://proceedings.mlr.press %V 48 %W PMLR %X Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications.
RIS
TY - CPAPER TI - Isotonic Hawkes Processes AU - Yichen Wang AU - Bo Xie AU - Nan Du AU - Le Song BT - Proceedings of The 33rd International Conference on Machine Learning PY - 2016/06/11 DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-wangg16 PB - PMLR SP - 2226 DP - PMLR EP - 2234 L1 - http://proceedings.mlr.press/v48/wangg16.pdf UR - http://proceedings.mlr.press/v48/wangg16.html AB - Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world data. To address this shortcoming, we propose an Isotonic-Hawkes process whose intensity function is modulated by an additional nonlinear link function. We also developed a novel iterative algorithm which learns both the nonlinear link function and other parameters provably. We showed that Isotonic-Hawkes processes can fit a variety of nonlinear patterns which cannot be captured by conventional Hawkes processes, and achieve superior empirical performance in real world applications. ER -
APA
Wang, Y., Xie, B., Du, N. & Song, L.. (2016). Isotonic Hawkes Processes. Proceedings of The 33rd International Conference on Machine Learning, in PMLR 48:2226-2234

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