# Causal discovery in heavy-tailed models

## TL;DR

This paper introduces a novel causal discovery method tailored for heavy-tailed data, leveraging extremal dependence asymmetries to infer causal structures even with latent variables, and demonstrates its effectiveness through theoretical guarantees and empirical tests.

## Contribution

It proposes the causal tail coefficient for extremal dependence analysis and develops a consistent, efficient algorithm for causal inference in heavy-tailed models, extending causal discovery to extreme value contexts.

## Key findings

- The causal tail coefficient reveals causal directions in heavy-tailed data.
- The proposed algorithm consistently recovers causal order in simulations.
- The method performs well on synthetic and real heavy-tailed datasets.

## Abstract

Causal questions are omnipresent in many scientific problems. While much progress has been made in the analysis of causal relationships between random variables, these methods are not well suited if the causal mechanisms only manifest themselves in extremes. This work aims to connect the two fields of causal inference and extreme value theory. We define the causal tail coefficient that captures asymmetries in the extremal dependence of two random variables. In the population case, the causal tail coefficient is shown to reveal the causal structure if the distribution follows a linear structural causal model. This holds even in the presence of latent common causes that have the same tail index as the observed variables. Based on a consistent estimator of the causal tail coefficient, we propose a computationally highly efficient algorithm that estimates the causal structure. We prove that our method consistently recovers the causal order and we compare it to other well-established and non-extremal approaches in causal discovery on synthetic and real data. The code is available as an open-access R package.