Variational bayesian inference for nonlinear hawkes process with gaussian process self-effects
- Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.
Author details: | Noa Malem-ShinitskiORCiDGND, Cesar Ojeda, Manfred OpperORCiDGND |
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DOI: | https://doi.org/10.3390/e24030356 |
ISSN: | 1099-4300 |
Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/35327867 |
Title of parent work (English): | Entropy |
Publisher: | MDPI |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/02/28 |
Publication year: | 2022 |
Release date: | 2024/02/02 |
Tag: | Bayesian inference; Gaussian process; point process |
Volume: | 24 |
Issue: | 3 |
Article number: | 356 |
Number of pages: | 22 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [318763901-SFB1294]; BIFOLD Berlin; Institute for the Foundations of Learning and Data [01IS18025A,; 01IS18037A] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Gold Open-Access |
DOAJ gelistet | |
License (German): | CC-BY - Namensnennung 4.0 International |