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

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. The eSCM provides a common foundation for the two main existing approaches to extremal causal modeling, the max-linear and the sum-linear structural causal models, recovering both as special cases within a single asymptotic formulation. More broadly, it 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 exploits this causal asymmetry and demonstrate its effectiveness on both simulated and real datasets.

arXiv commentAdded Corollary 2.6, which presents the approximation of eSCMs by probabilistic SCMs from a Poisson point process perspective. Added a comprehensive simulation study on the choice of the extremal subsample size in Appendix A.1