  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.
