论文标题
浅神经鹰队：霍克斯过程的非参数内核估计
Shallow Neural Hawkes: Non-parametric kernel estimation for Hawkes processes
论文作者
论文摘要
多维霍克斯过程（MHP）是一类自我和相互激动人心的点过程，可以找到广泛的应用 - 从地震的预测到高频交易中订单书的建模。本文做出了两个主要贡献，我们首先找到了霍克斯工艺的对数似然估计器的无偏估计器，以有效利用随机梯度下降方法，以最大程度地估计。第二个贡献是，我们提出了一个特定的单个隐藏层神经网络，用于对MHP的基础核的非参数估计。我们在合成数据集和实际数据集上评估了所提出的模型，并发现该方法比现有估计方法具有可比性或更好的性能。使用浅神经网络可确保我们不妥协Hawkes模型的解释性，同时又有灵活性来估计任何非标准的Hawkes激发内核。
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes two major contributions, we first find an unbiased estimator for the log-likelihood estimator of the Hawkes process to enable efficient use of the stochastic gradient descent method for maximum likelihood estimation. The second contribution is, we propose a specific single hidden layered neural network for the non-parametric estimation of the underlying kernels of the MHP. We evaluate the proposed model on both synthetic and real datasets, and find the method has comparable or better performance than existing estimation methods. The use of shallow neural network ensures that we do not compromise on the interpretability of the Hawkes model, while at the same time have the flexibility to estimate any non-standard Hawkes excitation kernel.
