Nonlinear Hawkes Process with Gaussian Process Self Effects
This work provides a more flexible and data-efficient model for point process analysis in domains like neuroscience or finance, though it is incremental as it builds on existing Bayesian inference for Hawkes processes.
The authors tackled the problem of modeling time-continuous point processes with flexible history dependence by proposing a Hawkes process with Gaussian Process self-effects, achieving a model that works well with scarce data and does not require estimating a branching structure for inference.
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 type 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 our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes. Efficient 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 three different domains and compare it to previously reported results.