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

Entropy

Manfred Opper¹  César Ojeda¹  Noa Malem-Shinitski² 

[1] Artificial Intelligence Group, Technische Universität Berlin, 10623 Berlin, Germany;Institute of Mathematics, University of Potsdam, 14476 Potsdam, Germany;

关键词: Bayesian inference;    point process;    Gaussian process;   

DOI  :  10.3390/e24030356

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown