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Article

Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects

1
Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany
2
Artificial Intelligence Group, Technische Universität Berlin, 10623 Berlin, Germany
3
Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, Birmingham B15 2TT, UK
*
Author to whom correspondence should be addressed.
Academic Editors: Udo Von Toussaint and Philip Broadbridge
Entropy 2022, 24(3), 356; https://doi.org/10.3390/e24030356
Received: 27 December 2021 / Revised: 9 February 2022 / Accepted: 22 February 2022 / Published: 28 February 2022
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. View Full-Text
Keywords: Bayesian inference; point process; Gaussian process Bayesian inference; point process; Gaussian process
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MDPI and ACS Style

Malem-Shinitski, N.; Ojeda, C.; Opper, M. Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects. Entropy 2022, 24, 356. https://doi.org/10.3390/e24030356

AMA Style

Malem-Shinitski N, Ojeda C, Opper M. Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects. Entropy. 2022; 24(3):356. https://doi.org/10.3390/e24030356

Chicago/Turabian Style

Malem-Shinitski, Noa, César Ojeda, and Manfred Opper. 2022. "Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects" Entropy 24, no. 3: 356. https://doi.org/10.3390/e24030356

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