自激点过程在相依事件中的建模及其应用

Modeling and Application of Self-Exciting Point Process in Dependent Events

摘要: 相依事件序列广泛存在于金融、社交网络等诸多领域，其事件间具有强烈的依赖性，使得传统事件序列建模方法难以准确刻画其动态特征。为了有效地描述事件间的依赖关系，基于自激点过程构建了扩展模型，将自激函数推广到指数函数和形式，并提出了分布式统计推断方法。通过将数据划分至多个节点进行并行计算，再聚合估计结果，解决了传统极大似然估计在大数据处理中计算成本高和效率低的问题，为自激点过程在大数据中的应用提供了新的解决方案。仿真实验结果表明，分布式估计在有限样本下与传统全局估计表现一致，同时将运行时间缩短约70%。在实证分析中，自激点过程模型有效刻画了Boston犯罪数据和IPTV用户点播行为数据的趋势，并将计算时间分别提升了约95%和64%。

Abstract: The sequence of dependent events is widely present in various fields, such as finance and social networks, where strong dependencies between events make it difficult for traditional event sequence modeling methods to accurately capture their dynamic characteristics. To effectively describe these dependencies, an extended model based on the self-exciting point process is constructed, generalizing the self-exciting function to a sum of exponential functions. A distributed statistical inference method is proposed, which divides the data across multiple nodes for parallel computation and then aggregates the estimation results. This approach addresses the high computational cost and low efficiency of traditional maximum likelihood estimation in big data processing, providing a new solution for applying self-exciting point processes to big data. Simulation experiments show that the distributed estimation performs consistently with traditional global estimation on limited samples while reducing runtime by approximately 70%. In empirical analysis, the self-exciting point process model effectively captures trends in Boston crime data and IPTV user on-demand behavior data, improving computation time by approximately 95% and 64%, respectively.