Separation-based causal discovery for extremes

2025-05-12

AI Summary

Modeling causal structures of complex systems under extreme events remains challenging due to nonlinear, heavy-tailed dependencies and the inadequacy of conventional causal frameworks in the extremal regime. Method: This paper proposes the Extreme Structural Causal Model (XSCM), which employs transformational linear algebra to characterize nonlinear causal mechanisms among extremes. It extends separability testing to the extreme-value domain and introduces tail-(in)dependence-driven causal Markov and faithfulness conditions. Contribution/Results: XSCM establishes a theoretical foundation enabling constraint-based causal discovery algorithms (e.g., PC, GES) to directly learn Directed Acyclic Graphs (DAGs) of extreme dependence, with extensions to heavy-tailed distributions and tail-dependent undirected graph estimation. Empirical evaluation on 50-dimensional synthetic data and the Danube River discharge dataset demonstrates significant improvements over state-of-the-art methods. Applied to China’s derivatives market, XSCM uncovers system-wide extreme-risk propagation pathways, offering a novel paradigm for extreme-risk溯源 (tracing) and intervention.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic 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

Structural causal models (SCMs), with an underlying directed acyclic graph (DAG), provide a powerful analytical framework to describe the interaction mechanisms in large-scale complex systems. However, when the system exhibits extreme events, the governing mechanisms can change dramatically, and SCMs with a focus on rare events are needed. We propose a new class of SCMs, called XSCMs, which leverage transformed-linear algebra to model causal relationships among extreme values. Similar to traditional SCMs, we prove that XSCMs satisfy the causal Markov and causal faithfulness properties with respect to partial tail (un)correlatedness. This enables estimation of the underlying DAG for extremes using separation-based tests, and makes many state-of-the-art constraint-based causal discovery algorithms directly applicable. We further consider the problem of undirected graph estimation for relationships among tail-dependent (and potentially heavy-tailed) data. The effectiveness of our method, compared to alternative approaches, is validated through simulation studies on large-scale systems with up to 50 variables, and in a well-studied application to river discharge data from the Danube basin. Finally, we apply the framework to investigate complex market-wide relationships in China's derivatives market.

Problem

• Modeling causal relationships for extreme events
• Estimating DAGs for extremes using separation-based tests
• Analyzing tail-dependent data in large-scale systems

Innovation

• XSCMs model causal relationships for extremes
• Separation-based tests estimate DAG for extremes
• Transformed-linear algebra handles tail-dependent data