Hawkes process papers notes
BY, 01 February 2018
Classic Paper
First proposed by Alan Hawkes as self-exciting point process. Hawkes and Oakes further developed a Poisson clustering process representation - very useful for simulation, declustering and order bounds.
Later Yosihiko Ogata used Hawkes process to model earthquake after-shocks events in his seminal papers on temporal and spatiotemporal cases. They also provide evaluation methods such as transformed time. For spatiotemporal, Voronoi cells are used to address the uneven distribution in space.
The estimation of Hawkes process is an interesting direction with many open problems. EM-Type algorithm proposed by Veen and Schoenberg is related to the nonparametric method by Marsan and Lengline. Many papers are looking for faster algorithms in the multivariate case because the number of parameters and data, such as a recent cumulants-based method. There is a good review paper by Alex Reinhard for Spatiotemporal Point processes.
Applications
Crime
George Mohler’s JASA paper uses nonparametric Hawkes process to model crimes in LA and another paper uses a KDE background method for Chicago crimes….. I am recently working on a gang violence intervention program in LA using multivariate Hawkes processes and also find this model is useful for retailation behaviors.
Network
Multivariate Hawkes processes (connection to Granger causality) are used to reconstruct networks. Examples: Email network using temporal Hawkes with background rate periodic in time (other choices of inhomogeneous background rate in time: KDE and log Gaussian Cox process); Bayesian Hawkes uses a temporal Hawkes with random graph prior; Beyond Mutual Excitation considers inhibitions; We have a recent paper considering spatiotemporal case. Interesting connection to dynamic graph embeddings.
Epidemic
Socal media
Many papers(see a review) are using Hawkes process to model contagious on social media such as retweeting. I got some interesting results when using Hawkes process to model tweet topics from NMF in a REU project. Currently working on other applications of Hawkes topic model.
Disease
Connection to SIR.