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.

翻译：本文介绍了非线性霍克斯过程神经网络(NNNH),这是一种基于神经网络的非参数性方法,以适应非线性霍克斯过程。我们的方法适合于分析大型数据集,在这些数据集中,各种事件表现出相互振奋和抑制的形态。NNNH方法模拟非线性霍克斯过程的单个内核和基强度,使用前线性神经网络供养,并通过尽量扩大日志类功能来联合校准网络的参数。我们利用Stochatic Gradient Eround来寻找最佳参数,为梯度提出一个公正的测算器,以及一个高效的计算方法。我们通过模拟数据和现实世界数据的数字实验来展示我们的方法的灵活性和准确性,并将它与最新的方法进行比较。我们的结果突出了NNHS方法在准确捕捉非线性霍克斯过程复杂性方面的有效性。</s>