FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels
This work addresses the need for efficient inference in temporal point processes for domains like neuroscience, offering a novel method that improves latency estimation, though it is incremental as it builds on existing Hawkes process models with a new solver.
The paper tackles the problem of efficient inference for Hawkes processes with general parametric kernels, which are needed for applications like neuroscience where latency estimation is crucial, and demonstrates through experiments that the proposed fast discretized gradient-based solver improves latency estimation compared to state-of-the-art methods.
Temporal point processes (TPP) are a natural tool for modeling event-based data. Among all TPP models, Hawkes processes have proven to be the most widely used, mainly due to their adequate modeling for various applications, particularly when considering exponential or non-parametric kernels. Although non-parametric kernels are an option, such models require large datasets. While exponential kernels are more data efficient and relevant for specific applications where events immediately trigger more events, they are ill-suited for applications where latencies need to be estimated, such as in neuroscience. This work aims to offer an efficient solution to TPP inference using general parametric kernels with finite support. The developed solution consists of a fast $\ell_2$ gradient-based solver leveraging a discretized version of the events. After theoretically supporting the use of discretization, the statistical and computational efficiency of the novel approach is demonstrated through various numerical experiments. Finally, the method's effectiveness is evaluated by modeling the occurrence of stimuli-induced patterns from brain signals recorded with magnetoencephalography (MEG). Given the use of general parametric kernels, results show that the proposed approach leads to an improved estimation of pattern latency than the state-of-the-art.