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

2025-07-31

AI Summary

Traditional probabilistic modeling fails in extreme-event causal inference, where conventional distributions are inadequate and causal direction is unidentifiable. To address this, we propose the extreme structural causal model (eSCM), which replaces standard distributions with exponential measures from extreme-value theory, introduces “activating variables” to capture the single large-jump mechanism underlying multivariate extremes, and defines extremal conditional independence to enable causal structure identification. Under natural assumptions, eSCM reveals causal asymmetry in extreme dependence—resolving, for the first time within an extreme-value framework, the fundamental problem of causal direction identifiability. Our inference method combines theoretical rigor with computational tractability, accurately recovering causal graphs on both synthetic and real-world extreme-event data (e.g., meteorological and financial extremes). This advances both the modeling fidelity and interpretability of complex extremal dependence structures.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Develops extremal structural causal models for extreme events
• Identifies causal direction asymmetry in extreme scenarios
• Proposes method leveraging causal asymmetry for inference

Innovation

• eSCM uses exponent measure for extremes
• Activation variables abstract big-jump principle
• Causal asymmetry enables direction identifiability