Heavy Tailed Homogeneous Structural Causal Models

TL;DR

This paper introduces the HT-HSCM framework for causal discovery in heavy-tailed systems, leveraging tail information to identify causal structures and develop recursive algorithms for model recovery.

Contribution

The paper presents a unified framework generalizing heavy-tailed models and introduces causal tail coefficients for complete causal ordering identification.

Findings

Causal tail coefficients identify the full ancestral partial order.

A recursive algorithm recovers ancestral impulse-responses from tail coefficients.

The framework applies to heavy-tailed linear and max-linear models.

Abstract

We consider causal discovery in structural causal models driven by heavy-tailed noise, where extremes carry important information about causal direction. We introduce the Heavy-Tailed Homogeneous Structural Causal Model (HT-HSCM), a unified framework that generalizes heavy-tailed linear and max-linear models. We demonstrate that causal tail coefficients identify the complete ancestral partial order of the underlying directed acyclic graph. We also formulate a recursive algorithm for recovering quantities associated with the model called ancestral impulse-responses from the causal tail coefficients. Our results provide a general and theoretically justified framework for causal discovery in heavy-tailed systems.