Hawkes Processes with Delayed Granger Causality

TL;DR

This paper introduces a novel Hawkes process model that explicitly incorporates delayed Granger causal effects, enabling more accurate event prediction and causal inference by modeling time lags as latent variables.

Contribution

It proposes a new model with identifiable delay parameters and a VAE-based estimation method for inferring the distribution of causal time lags.

Findings

Accurate inference of time-lag distributions on synthetic data

Improved event prediction performance on real datasets

Effective root cause analysis through lag distribution insights

Abstract

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.