Hawkes Processes with Delayed Granger Causality
This work addresses the need for more flexible causal analysis in event data, such as in finance or neuroscience, by modeling time delays, though it is incremental as it builds on existing Hawkes process frameworks.
The paper tackles the problem of modeling delayed Granger causality in multivariate Hawkes processes by explicitly incorporating time lags, proving identifiability and developing a VAE-based method for posterior inference, achieving promising results in event prediction and time-lag accuracy on synthetic and real data.
We aim to explicitly model the delayed Granger causal effects based on multivariate Hawkes processes. The idea is inspired by the fact that a causal event usually takes some time to exert an effect. Studying this time lag itself is of interest. Given the proposed model, we first prove the identifiability of the delay parameter under mild conditions. We further investigate a model estimation method under a complex setting, where we want to infer the posterior distribution of the time lags and understand how this distribution varies across different scenarios. We treat the time lags as latent variables and formulate a Variational Auto-Encoder (VAE) algorithm to approximate the posterior distribution of the time lags. By explicitly modeling the time lags in Hawkes processes, we add flexibility to the model. The inferred time-lag posterior distributions are of scientific meaning and help trace the original causal time that supports the root cause analysis. We empirically evaluate our model's event prediction and time-lag inference accuracy on synthetic and real data, achieving promising results.