Causal Discovery in Hawkes Processes by Minimum Description Length

TL;DR

This paper introduces a novel MDL-based method for discovering causal influence networks in multi-dimensional Hawkes processes, demonstrating improved accuracy on synthetic data and real-world financial data.

Contribution

It formulates causal discovery as a model selection problem using MDL and proposes a Monte-Carlo algorithm for inference, outperforming existing methods.

Findings

Superior causal graph discovery on synthetic data

Consistent results with expert knowledge on financial data

Effective in high-frequency data modeling

Abstract

Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence network among the dimensions of multi-dimensional temporal processes is of high importance in disciplines where a high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multi-dimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method incausal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts knowledge.