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.

翻译：我们提出了一种新的极值结构因果模型形式，称为极值结构因果模型（eSCM）。与传统结构因果模型中由概率分布支配随机性不同，eSCM采用指数测度——一种在多元极值分析中自然出现的无限质量律。该框架的核心是激活变量，它抽象了单次大跳跃原理，并结合额外随机化以丰富eSCM律的类别。这一形式涵盖了在最近提出的极值条件独立性概念下所有可能的有向图模型律。我们还识别了自然假设下eSCM固有的非对称性，从而能够识别因果关系方向——这是因果推断中的核心挑战。最后，我们提出了一种利用这种因果不对称性的方法，并在模拟和真实数据集中证明了其有效性。