A neural network based model for multi-dimensional non-linear Hawkes processes

Abstract

This paper introduces the Neural Network for Non-linear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit non-linear Hawkes processes. Our method is suitable for analysing large datasets in which events exhibit both mutually-exciting and inhibitive patterns. The NNNH approach models the individual kernels and the base intensity of the non-linear Hawkes process using feed forward neural networks and jointly calibrates the parameters of the networks by maximizing the log-likelihood function. We utilize Stochastic Gradient Descent to search for the optimal parameters and propose an unbiased estimator for the gradient, as well as an efficient computation method. We demonstrate the flexibility and accuracy of our method through numerical experiments on both simulated and real-world data, and compare it with state-of-the-art methods. Our results highlight the effectiveness of the NNNH method in accurately capturing the complexities of non-linear Hawkes processes.