# Tail dependence of recursive max-linear models with regularly varying noise variables

## TL;DR

This paper investigates how to identify the causal structure of recursive max-linear models with heavy-tailed noise by analyzing their tail dependence matrices, providing algorithms for model and DAG recovery.

## Contribution

It introduces methods to recover the minimum DAG and models from tail dependence matrices, advancing causal inference in heavy-tailed settings.

## Key findings

- Minimum DAG can be recovered if causal order is known.
- Identifiability of the DAG from tail dependence matrix is established.
- Algorithms are provided for model and DAG identification.

## Abstract

Recursive max-linear structural equation models with regularly varying noise variables are considered. Their causal structure is represented by a directed acyclic graph (DAG). The problem of identifying a recursive max-linear model and its associated DAG from its matrix of pairwise tail dependence coefficients is discussed. For example, it is shown that if a causal ordering of the associated DAG is additionally known, then the minimum DAG representing the recursive structural equations can be recovered from the tail dependence matrix. For the relevant subclass of recursive max-linear models, identifiability of the associated minimum DAG from the tail dependence matrix and the initial nodes is shown. Algorithms find the associated minimum DAG for the different situations. Furthermore, given a tail dependence matrix, an algorithm outputs all compatible recursive max-linear models and their associated minimum DAGs.