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Hawkes Processes with Stochastic Excitations

Young Lee,Kar Wai Lim,Cheng Soon Ong

Published 2016 in International Conference on Machine Learning

ABSTRACT

We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate each other with correlated levels of contagion. We generalize a recent algorithm for simulating draws from Hawkes processes whose levels of excitation are stochastic processes, and propose a hybrid Markov chain Monte Carlo approach for model fitting. Our sampling procedure scales linearly with the number of required events and does not require stationarity of the point process. A modular inference procedure consisting of a combination between Gibbs and Metropolis Hastings steps is put forward. We recover expectation maximization as a special case. Our general approach is illustrated for contagion following geometric Brownian motion and exponential Langevin dynamics.

PUBLICATION RECORD

  • Publication year

    2016

  • Venue

    International Conference on Machine Learning

  • Publication date

    2016-06-19

  • Fields of study

    Mathematics, Computer Science

  • Identifiers
    arXiv 1609.06831
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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