Hawkes Process

Hawkes processes are mathematical models used to analyze sequences of events where the occurrence of one event influences the probability of future events, capturing self-exciting and mutually-exciting dynamics. Current research focuses on improving model robustness to noisy data, enhancing the ability to handle complex interactions and nonlinearities (e.g., through neural network integration, such as Transformer Hawkes Processes and Mamba Hawkes Processes), and developing efficient inference techniques (e.g., using Bayesian methods, score matching, or Frank-Wolfe algorithms). These advancements are significantly impacting fields like finance, healthcare, and social network analysis by enabling more accurate modeling of event sequences and improved prediction capabilities.