196 research outputs found
FaDIn: Fast Discretized Inference for Hawkes Processes with General Parametric Kernels
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 simplicity and computational ease 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 certain 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 L2 gradient-based solver leveraging a
discretized version of the events. After supporting the use of discretization
theoretically, the statistical and computational efficiency of the novel
approach is demonstrated through various numerical experiments. Finally, the
effectiveness of the method 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 a more plausible estimation of
pattern latency compared to the state-of-the-art
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