Nonlinear Causal Discovery for Grouped Data

2025/06/05 by Konstantin Göbler, Göbler, Konstantin, Tobias Windisch +3 · 1 voice · 2 citations
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #cs.LG #stat.ME #stat.ML

paper · pdf · doi:10.48550/arxiv.2506.05120

openalex publication_date 2025/06/05 · arxiv published 2025/06/05 · arxiv updated 2025/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Adjustment Identification Distance: A gadjid for Causal Structure Learning
• causalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery
• Foundations of Causal Discovery on Groups of Variables
• Vector causal inference between two groups of variables
• Score matching enables causal discovery of nonlinear additive noise models
• Causal Effect Identification in Cluster DAGs
• Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game
• Robust Learning with the Hilbert-Schmidt Independence Criterion
• Gradient-Based Neural DAG Learning
• DAGs with NO TEARS: Continuous Optimization for Structure Learning
• Structure Learning in Graphical Modeling
• Multi-Level Cause-Effect Systems
• Order-independent constraint-based causal structure learning
• Estimating a Causal Order among Groups of Variables in Linear Models
• Group Sparse Additive Models
• Testing whether linear equations are causal: A free probability theory approach
• Identifiability of Causal Graphs using Functional Models
• DirectLiNGAM: A direct method for learning a linear non-Gaussian structural equation model
• Exact block-wise optimization in group lasso and sparse group lasso for linear regression
• Telling cause from effect based on high-dimensional observations
• Multi-Task Feature Learning Via Efficient l2,1-Norm Minimization
• On the Identifiability of the Post-Nonlinear Causal Model
• Sparse Additive Models
• Recovery algorithms for vector valued data with joint sparsity constraints
• Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks
• Convergent and discriminant validation by the multitrait-multimethod matrix.

Cited by

• Cluster-Dags as Powerful Background Knowledge For Causal Discovery
• From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables

Discussions

• Causal discovery on R^n, n > 1... My reactions are (1) I'm glad work on that is progressing, most of the universe isn't decomposable into independent scalars, (2) it doesn't feel we have well-known st [bsky, 1 points, 0 comments]

Related

• Estimating a Causal Order among Groups of Variables in Linear Models
• From Causal Pairs to Causal Graphs
• Learning causal graphs using variable grouping according to ancestral relationship
• Hierarchical Causal Structure Learning
• Vector causal inference between two groups of variables