  Multi-dimensional Hawkes process (MHP) is a class of self and mutually
exciting point processes that find wide range of applications -- from
prediction of earthquakes to modelling of order books in high frequency
trading. This paper makes two major contributions, we first find an unbiased
estimator for the log-likelihood estimator of the Hawkes process to enable
efficient use of the stochastic gradient descent method for maximum likelihood
estimation. The second contribution is, we propose a specific single hidden
layered neural network for the non-parametric estimation of the underlying
kernels of the MHP. We evaluate the proposed model on both synthetic and real
datasets, and find the method has comparable or better performance than
existing estimation methods. The use of shallow neural network ensures that we
do not compromise on the interpretability of the Hawkes model, while at the
same time have the flexibility to estimate any non-standard Hawkes excitation
kernel.
