Isotonic Hawkes Processes
Yichen Wang, Bo Xie, Nan Du, Le Song
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.
BibTeX
@InProceedings{pmlr-v48-wangg16,
title = {Isotonic Hawkes Processes},
author = {Wang, Yichen and Xie, Bo and Du, Nan and Song, Le},
booktitle = {Proceedings of The 33rd International Conference on Machine Learning},
pages = {2226--2234},
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/wangg16.pdf},
url = {https://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.}
}