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：本文提出了非线性Hawkes过程的神经网络模型（NNNH），这是一种基于神经网络的非参数方法，用于拟合非线性Hawkes过程。本方法适用于分析同时呈现相互激励与抑制模式的大规模事件数据集。NNNH方法通过前馈神经网络对非线性Hawkes过程的个体核函数与基强度进行建模，并通过最大化对数似然函数联合校准网络参数。我们采用随机梯度下降法搜索最优参数，提出了梯度的无偏估计量及高效计算方法。通过模拟数据与真实数据的数值实验，我们验证了该方法的灵活性与准确性，并将其与现有最优方法进行对比。实验结果表明，NNNH方法能够有效捕捉非线性Hawkes过程的复杂性。