Modeling Event Dynamics by Self-Exciting Processes with Random Memory

2026-01-12

AI Summary

This study addresses the limitations of conventional inter-event time–based models in capturing self-excitation and intra-cluster dependencies in sports events, particularly their inability to account for uncertainty in the duration of self-exciting effects. To overcome this, the authors propose an extended Hawkes process incorporating a stochastic duration of self-excitation. By introducing a random memory mechanism, the model endows the decay of self-exciting effects with dynamic uncertainty, thereby better reflecting real-world event sequences. Parameter inference is performed via maximum likelihood estimation, accompanied by a tailored simulation algorithm. Experiments on corner kick data from the 2019 Chinese Super League demonstrate that the proposed method effectively captures the self-exciting dynamics within event clusters, offering a generalizable modeling framework applicable to domains such as sports analytics, criminology, and epidemiology.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Event history data from sports competitions have recently drawn increasing attention in sports analytics to generate data-driven strategies. Such data often exhibit self-excitation in the event occurrence and dependence within event clusters. The conventional event models based on gap times may struggle to capture those features. In particular, while consecutive events may occur within a short timeframe, the self-excitation effect caused by previous events is often transient and continues for a period of uncertain time. This paper introduces an extended Hawkes process model with random self-excitation duration to formulate the dynamics of event occurrence. We present examples of the proposed model and procedures for estimating the associated model parameters. We employ the collection of the corner kicks in the games of the 2019 regular season of the Chinese Super League to motivate and illustrate the modeling and its usefulness. We also design algorithms for simulating the event process under proposed models. The proposed approach can be adapted with little modification in many other research fields such as Criminology and Infectious Disease.

Problem

• self-excitation
• event history data
• Hawkes process
• random memory
• event dynamics

Innovation

• Hawkes process
• self-excitation
• random memory
• event dynamics
• temporal point process