A neural network based model for multi-dimensional nonlinear Hawkes processes
This work addresses the challenge of accurately capturing complex event dynamics in fields like finance or neuroscience, representing an incremental improvement by applying neural networks to a known bottleneck in existing Hawkes process models.
This paper tackled the problem of modeling multi-dimensional nonlinear Hawkes processes with mutually-exciting and inhibitive patterns in large datasets, and introduced the Neural Network for Nonlinear Hawkes processes (NNNH) method, which demonstrated flexibility and accuracy in numerical experiments on simulated and real-world data compared to state-of-the-art methods.
This paper introduces the Neural Network for Nonlinear Hawkes processes (NNNH), a non-parametric method based on neural networks to fit nonlinear Hawkes processes. Our method is suitable for analyzing 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 nonlinear 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 nonlinear Hawkes processes.