Nonlinear Causal Discovery for Grouped Data

2025-06-05

AI Summary

Existing nonlinear causal discovery methods primarily target scalar variables, rendering them inadequate for real-world scenarios—such as neuroscience and industrial manufacturing—where causal units are naturally groups of variables (i.e., random vectors). Method: This paper introduces the first extension of the nonlinear additive noise model (ANM) to the random vector setting, proposing a two-stage framework: (1) inferring inter-group causal order via vector-level independence testing, and (2) searching for the optimal causal graph under the inferred order constraint. The approach integrates vector independence testing, causal-order-guided graph structure search, and domain-adapted validation. Contribution/Results: Experiments demonstrate that our method significantly outperforms scalar-based baselines on synthetic data and successfully recovers causal dependencies among multivariate sensor groups in real production lines. It further validates the plausibility of prior causal orders, establishing an interpretable and scalable paradigm for group-level causal modeling.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Inferring cause-effect relationships from observational data has gained significant attention in recent years, but most methods are limited to scalar random variables. In many important domains, including neuroscience, psychology, social science, and industrial manufacturing, the causal units of interest are groups of variables rather than individual scalar measurements. Motivated by these applications, we extend nonlinear additive noise models to handle random vectors, establishing a two-step approach for causal graph learning: First, infer the causal order among random vectors. Second, perform model selection to identify the best graph consistent with this order. We introduce effective and novel solutions for both steps in the vector case, demonstrating strong performance in simulations. Finally, we apply our method to real-world assembly line data with partial knowledge of causal ordering among variable groups.

Problem

• Extend causal discovery to grouped variables, not just scalars
• Develop method to infer causal order among random vectors
• Apply approach to real-world data with partial ordering

Innovation

• Extends nonlinear additive noise models to vectors
• Two-step causal graph learning approach
• Effective solutions for vector causal order