Hierarchical Causal Structure Learning

2025-11-25

AI Summary

Existing causal structure learning methods struggle with hierarchical multilevel data—e.g., settings where individual-level and group-level variables coexist. This paper introduces the first causal structure learning framework specifically designed for multilevel data, extending nonlinear structural causal models (SCMs) to explicitly encode group-specific causal mechanisms and unobserved confounders. Our approach integrates the additive noise assumption with a hierarchical graphical model, enabling identifiable causal discovery in scenarios featuring both unit-level and group-level variables. Theoretically, we establish identifiability guarantees for multilevel causal structures under mild assumptions. Algorithmically, we develop an efficient learning procedure and implement it in the open-source R package HSCM, publicly available on CRAN. Empirical evaluation on real-world multilevel applications—including agricultural case studies—demonstrates the method’s effectiveness and accuracy in recovering ground-truth causal relationships across levels.

Technology Category

Machine Learning: Causal LearningReasoning under Uncertainty: CausalityKnowledge Representation and Reasoning: Action, Change, and Causality

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphsWeb Mining and Content Analysis: Bridging structured and unstructured dataSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Traditional statistical approaches primarily aim to model associations between variables, but many scientific and practical questions require causal methods instead. These approaches rely on assumptions about an underlying structure, often represented by a directed acyclic graph (DAG). When all variables are measured at the same level, causal structures can be learned using existing techniques. However, no suitable methods exist when data are organized hierarchically or across multiple levels. This paper addresses such cases, where both unit-level and group-level variables are present. These multi-level structures frequently arise in fields such as agriculture, where plants (units) grow within different environments (groups). Building on nonlinear structural causal models, or additive noise models, we propose a method that accommodates unobserved confounders as well as group-specific causal functions. The approach is implemented in the R package HSCM, available at https://CRAN.R-project.org/package=HSCM.

Problem

• Develops hierarchical causal learning for multi-level data structures
• Addresses unit-level and group-level variables with unobserved confounders
• Provides method when traditional DAG approaches fail on hierarchical data

Innovation

• Hierarchical causal structure learning with multi-level variables
• Nonlinear structural models accommodating unobserved confounders
• Group-specific causal functions implemented in R package