Online Learning for Multivariate Hawkes Processes
Abstract
We develop a nonparametric and online learning algorithm that estimates the triggering functions of a multivariate Hawkes process (MHP). The approach we take approximates the triggering function $f_{i,j}(t)$ by functions in a reproducing kernel Hilbert space (RKHS), and maximizes a time-discretized version of the log-likelihood, with Tikhonov regularization. Theoretically, our algorithm achieves an $\calO(\log T)$ regret bound. Numerical results show that our algorithm offers a competing performance to that of the nonparametric batch learning algorithm, with a run time comparable to the parametric online learning algorithm.
Cite
Text
Yang et al. "Online Learning for Multivariate Hawkes Processes." Neural Information Processing Systems, 2017.Markdown
[Yang et al. "Online Learning for Multivariate Hawkes Processes." Neural Information Processing Systems, 2017.](https://mlanthology.org/neurips/2017/yang2017neurips-online/)BibTeX
@inproceedings{yang2017neurips-online,
title = {{Online Learning for Multivariate Hawkes Processes}},
author = {Yang, Yingxiang and Etesami, Jalal and He, Niao and Kiyavash, Negar},
booktitle = {Neural Information Processing Systems},
year = {2017},
pages = {4937-4946},
url = {https://mlanthology.org/neurips/2017/yang2017neurips-online/}
}