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

Joseph, S and Jain, S (2024) A neural network based model for multi-dimensional non-linear Hawkes processes. In: Journal of Computational and Applied Mathematics, 447 .

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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. © 2024 Elsevier B.V.

Item Type:	Journal Article
Publication:	Journal of Computational and Applied Mathematics
Publisher:	Elsevier B.V.
Additional Information:	The copyright for this article belongs to authors.
Keywords:	E-learning; Gradient methods; Numerical methods; Stochastic systems, Hawkes process with inhibition; Multi dimensional; Network-based modeling; Neural network for hawkes process; Neural-networks; Non linear; Non-linear hawkes process; Nonparametric methods; Online learning; Online learning for hawkes process, Large datasets
Department/Centre:	Division of Interdisciplinary Sciences > Management Studies
Date Deposited:	20 May 2024 11:55
Last Modified:	20 May 2024 11:55
URI:	https://eprints.iisc.ac.in/id/eprint/84732

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