Mean-field inference of Hawkes point processes
This provides an efficient solution for parameter estimation in Hawkes processes, which is useful in fields like finance or neuroscience, though it is incremental as it builds on existing mean-field approximations.
The authors tackled the problem of estimating parameters for high-dimensional Hawkes point processes by proposing a fast mean-field approximation method that works when intensity fluctuations are small, achieving comparable precision to the Maximum Likelihood Estimator with significantly improved computation speed.
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of the system is high or when the fluctuations are self-averaging due to the large number of past events they involve. In such a regime the estimation of a Hawkes process can be mapped on a least-squares problem for which we provide an analytic solution. Though this estimator is biased, we show that its precision can be comparable to the one of the Maximum Likelihood Estimator while its computation speed is shown to be improved considerably. We give a theoretical control on the accuracy of our new approach and illustrate its efficiency using synthetic datasets, in order to assess the statistical estimation error of the parameters.