LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data

2024-10-25

arXiv.org

AI Summary

Discovering causal DAGs from temporal observational data in dynamic nonlinear systems remains challenging, as existing methods rely on combinatorial search and suffer from exponential computational complexity in high-dimensional settings. Method: We propose ACML-DGPL—a unified framework comprising (i) a quasi-maximum-likelihood scoring function with theoretical guarantees of DAG equivalence to the true causal structure; (ii) an ACML module for causal mask learning, leveraging Gumbel-Sigmoid differentiable masks and asymptotically causal-prior vectors; and (iii) a DGPL module for dynamic graph parameter learning, employing decomposed parameterization and algebraic acyclicity constraints to enable unconstrained, efficient, and scalable optimization. Contribution/Results: Evaluated on multiple synthetic and real-world benchmarks, ACML-DGPL consistently outperforms state-of-the-art methods—achieving high accuracy and low computational overhead even in high-dimensional regimes—demonstrating its robustness and interpretability as a practical tool for dynamic causal discovery.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: ML for personalized search and recommendations

Abstract

Discovering the underlying Directed Acyclic Graph (DAG) from time series observational data is highly challenging due to the dynamic nature and complex nonlinear interactions between variables. Existing methods typically search for the optimal DAG by optimizing an objective function but face scalability challenges, as their computational demands grow exponentially with the dimensional expansion of variables. To this end, we propose LOCAL, a highly efficient, easy-to-implement, and constraint-free method for recovering dynamic causal structures. LOCAL is the first attempt to formulate a quasi-maximum likelihood-based score function for learning the dynamic DAG equivalent to the ground truth. Building on this, we introduce two adaptive modules that enhance the algebraic characterization of acyclicity: Asymptotic Causal Mask Learning (ACML) and Dynamic Graph Parameter Learning (DGPL). ACML constructs causal masks using learnable priority vectors and the Gumbel-Sigmoid function, ensuring DAG formation while optimizing computational efficiency. DGPL transforms causal learning into decomposed matrix products, capturing dynamic causal structure in high-dimensional data and improving interpretability. Extensive experiments on synthetic and real-world datasets demonstrate that LOCAL significantly outperforms existing methods and highlight LOCAL's potential as a robust and efficient method for dynamic causal discovery.

Problem

• Infer causal structure from time series data
• Overcome scalability challenges in DAG discovery
• Enhance interpretability of dynamic causal structures

Innovation

• Quasi-maximum likelihood-based score function
• Asymptotic Causal Mask Learning (ACML)
• Dynamic Graph Parameter Learning (DGPL)