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/}
}