# Hawkes Processes with Delayed Granger Causality

arXiv: https://arxiv.org/abs/2308.06106 · HTML: https://mlsanity.com/paper/2308.06106/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 11 Aug 2023.

## Builds on (most cited first, 8 of 8)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Modeling The Intensity Function Of Point Process Via Recurrent Neural Networks](https://mlsanity.com/paper/1705.08982/) (2017)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Uncovering Causality from Multivariate Hawkes Integrated Cumulants](https://mlsanity.com/paper/1607.06333/) (2016)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Variable-lag Granger Causality for Time Series Analysis](https://mlsanity.com/paper/1912.10829/) (2019)
- [Inference of multivariate exponential Hawkes processes with inhibition and application to neuronal activity](https://mlsanity.com/paper/2205.04107/) (2022)

## Abstract (arXiv)

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.