NeuroMem-FHP：一种用于分数阶霍克斯过程参数估计的无似然深度学习框架
NeuroMem-FHP: A Likelihood-Free Deep Learning Framework for Parameter Estimation of Fractional Hawkes Process
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中文总结 AI 辅助
本文提出NeuroMem-FHP框架，用LSTM网络和Transformer直接从到达间隔时间序列估计分数阶霍克斯过程参数，无需似然优化。实验表明其优于经典MLE方法，在真实数据集上也表现良好，为FHP参数估计提供了准确高效的替代方法。
中文摘要 AI 辅助
在本文中，我们提出了基于深度学习的NeuroMem-FHP框架，用于估计分数阶霍克斯过程（FHP）的参数，FHP是一种自激发点过程，通过分数阶米塔格-莱夫勒激发核捕获长程相关性。开发了两种神经架构，即长短期记忆（LSTM）网络和Transformer，以直接从到达间隔时间序列估计模型参数$(\mu,\gamma,\alpha,\beta)$，而无需进行计算密集型的似然优化。在合成数据上的实验表明，这两种神经模型均显著优于经典的最大似然估计（MLE）方法，Transformer实现了最高的估计精度（MSE = 0.1634），其次是LSTM（MSE = 0.1752），而MLE的MSE为2.8032。消融研究进一步考察了关键超参数对模型性能的影响。所提出的框架还应用于两个真实世界的高频数据集，即苹果公司全国最佳出价和要价交易数据以及蒙哥马利县911紧急呼叫记录。使用预测验证方法，从估计参数模拟的事件序列紧密再现了观测数据的经验分布、尾部行为和时间依赖结构。这些结果表明，基于Transformer的参数估计为FHP的传统估计技术提供了一种准确且高效的替代方法，并为建模具有长记忆动态的事件驱动系统提供了一个有前景的框架。
英文摘要
In this paper, we propose deep learning based NeuroMem-FHP framework for estimating the parameters of the fractional Hawkes process (FHP), a self-exciting point process that captures long-range dependence through a fractional Mittag-Leffler excitation kernel. Two neural architectures, namely a Long Short-Term Memory (LSTM) network and a Transformer, are developed to estimate the model parameters $(μ,γ,α,β)$ directly from sequences of inter-arrival times without requiring computationally intensive likelihood optimization. Experiments on synthetic data that both neural models significantly outperform the classical Maximum Likelihood Estimation (MLE) method, with the Transformer achieving the highest estimation accuracy (MSE = $0.1634$), followed by the LSTM (MSE = $0.1752$), compared to MLE (MSE = $2.8032$). An ablation study further examines the effects of key hyperparameters on model performance. The proposed framework is also on two real-world high-frequency datasets, namely AAPL NBBO transaction data and Montgomery County 911 emergency call records. Using a predictive validation approach, event sequences simulated from the estimated parameters closely reproduce the empirical distribution, tail behavior, and temporal dependence structure of the observed data. These results demonstrate that Transformer-based parameter estimation provides an accurate and efficient alternative to conventional estimation techniques for FHP and offers a promising framework for modeling event-driven systems with long-memory dynamics.
发表机构
- Indian Institute of Management Indore（印度管理学院印多尔分校）
机构由 AI 辅助整理，请以论文原文为准。
