Learning Granger Causality for Hawkes Processes

TL;DR

This paper introduces a novel method for learning Granger causality in Hawkes processes by representing impact functions with basis functions and using group sparsity, enabling simultaneous learning of causality graphs and triggering patterns.

Contribution

The paper presents a new approach combining basis function representation, group sparsity, and an adaptive algorithm for effective Granger causality learning in Hawkes processes.

Findings

Successfully recovers Granger causality graphs from synthetic data.

Effectively learns triggering patterns in real-world data.

Outperforms existing methods in accuracy and interpretability.

Abstract

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We reveal the relationship between Hawkes process's impact function and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions' coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the flexibility of our model allows to incorporate the clustering structure event types into learning framework. We analyze our learning algorithm and propose an adaptive procedure to select basis functions. Experiments on both synthetic and real-world data show that our method can learn the Granger causality graph and the triggering patterns of the Hawkes processes simultaneously.