Structural Causal Models for Extremes: an Approach Based on Exponent Measures

TL;DR

This paper introduces extremal structural causal models (eSCM) that leverage exponent measures to analyze multivariate extremes, enabling causal inference and direction identifiability.

Contribution

It presents a novel framework for causal modeling of extremes using exponent measures, including methods for causal direction identification.

Findings

eSCMs encompass all laws of directed graphical models under extremal conditional independence.

The proposed method effectively identifies causal directions in simulated and real data.

eSCMs reveal an inherent asymmetry useful for causal inference in extreme value analysis.

Abstract

We introduce a new formulation of structural causal models for extremes, called the extremal structural causal model (eSCM). Unlike conventional structural causal models, where randomness is governed by a probability distribution, eSCMs use an exponent measure, an infinite-mass law that naturally arises in the analysis of multivariate extremes. Central to this framework are activation variables, which abstract the single-big-jump principle, along with additional randomization that enriches the class of eSCM laws. This formulation encompasses all possible laws of directed graphical models under the recently introduced notion of extremal conditional independence. We also identify an inherent asymmetry in eSCMs under natural assumptions, enabling the identifiability of causal directions, a central challenge in causal inference. Finally, we propose a method that utilizes this causal asymmetry and demonstrate its effectiveness in both simulated and real datasets.