Causal discovery in heavy-tailed linear structural equation models via scalings

TL;DR

This paper introduces a new causal discovery method for heavy-tailed linear structural equation models using extremal angular measure scalings, with proven consistency and competitive performance on real data.

Contribution

It proposes a novel causal discovery algorithm based on extremal angular measure scalings for models with heavy-tailed noise, and demonstrates its effectiveness and consistency.

Findings

The method is consistent in identifying causal directions.

Simulation studies show competitive performance against existing extremal methods.

Application to river discharge data validates practical utility.

Abstract

Causal dependence modelling of multivariate extremes is intended to improve our understanding of the relationships amongst variables associated with rare events. Regular variation provides a standard framework in the study of extremes. This paper concerns the linear structural equation model with regularly varying noise variables. We focus on extreme observations generated from such a model and propose a causal discovery method based on the scaling parameters of its extremal angular measure. We implement the method as an algorithm, establish its consistency and evaluate it by simulation and by application to river discharge datasets. Comparison with the only alternative extremal method for such model reveals its competitive performance.