A simple demo is in Code/Simple_Example.ipynb
which contains synthetic data generation and model fitting.
Code/Data_Generator_Model_Fitting.ipynb presents more examples.
We provide some tools for neuroscience data, including data download script, data exploration, data preprocessing and model fitting.
The scripts are under Code/neuroscience.
Reference: Short-term Temporal Dependency Detection under Heterogeneous Event Dynamic with Hawkes Processes Yu Chen, Fengpei Li, Anderson Schneider, Yuriy Nevmyvaka, Asohan Amarasingham, Henry Lam, Conference on Uncertainty in Artificial Intelligence (UAI), 2023
Abstract: Many event sequence data exhibit mutually exciting or inhibiting patterns. Reliable detection of such temporal dependency is crucial for scientific investigation. The \textit{de facto} model is the Multivariate Hawkes Process (MHP), whose impact function naturally encodes a causal structure in Granger causality. However, the vast majority of existing methods use direct or nonlinear transform of \textit{standard} MHP intensity with constant baseline, inconsistent with real-world data. Under irregular and unknown heterogeneous intensity, capturing temporal dependency is hard as one struggles to distinguish the effect of mutual interaction from that of intensity fluctuation. In this paper, we address the short-term temporal dependency detection issue. We show the maximum likelihood estimation (MLE) for cross-impact from MHP has an error that can not be eliminated but may be reduced by order of magnitude, using heterogeneous intensity not of the target HP but of the interacting HP. Then we proposed a robust and computationally-efficient method modified from MLE that does not rely on the prior estimation of the heterogeneous intensity and is thus applicable in a data-limited regime (e.g., few-shot, no repeated observations). Extensive experiments on various datasets show that our method outperforms existing ones by notable margins, with highlighted novel applications in neuroscience.