Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes

ECML-PKDD 2014 pp. 161-176

doi:10.1007/978-3-662-44851-9_11 /ecmlpkdd/2014/lemonnier2014ecmlpkdd-nonparametric/

Abstract

In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on nonparametric learning and propose a novel algorithm called MEMIP (Markovian Estimation of Mutually Interacting Processes) that makes use of polynomial approximation theory and self-concordant analysis in order to learn both triggering kernels and base intensities of events. Moreover, considering that N historical observations are available, the algorithm performs log-likelihood maximization in O(N) operations, while the complexity of non-Markovian methods is in O(N2). Numerical experiments on simulated data, as well as real-world data, show that our method enjoys improved prediction performance when compared to state-of-the art methods like MMEL and exponential kernels.

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Text

Lemonnier and Vayatis. "Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014. doi:10.1007/978-3-662-44851-9_11

Markdown

[Lemonnier and Vayatis. "Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2014.](https://mlanthology.org/ecmlpkdd/2014/lemonnier2014ecmlpkdd-nonparametric/) doi:10.1007/978-3-662-44851-9_11

BibTeX

@inproceedings{lemonnier2014ecmlpkdd-nonparametric,
  title     = {{Nonparametric Markovian Learning of Triggering Kernels for Mutually Exciting and Mutually Inhibiting Multivariate Hawkes Processes}},
  author    = {Lemonnier, Rémi and Vayatis, Nicolas},
  booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
  year      = {2014},
  pages     = {161-176},
  doi       = {10.1007/978-3-662-44851-9_11},
  url       = {https://mlanthology.org/ecmlpkdd/2014/lemonnier2014ecmlpkdd-nonparametric/}
}