LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data (2410.19464v4)

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.

• The paper introduces a quasi-maximum likelihood framework that enhances the accuracy of causal inference in complex time series data.
• It integrates adaptive modules, including ACML and DGPL, to efficiently construct Directed Acyclic Graphs without heavy computational constraints.
• Experimental results show significant gains in TPR, SHD, and F1 scores, outperforming state-of-the-art methods on both synthetic and real datasets.

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

Introduction and Motivation

The paper introduces a novel method called LOCAL for inferring causal structures from time series data. This approach addresses significant challenges associated with discovering Directed Acyclic Graphs (DAGs) from observational data, particularly in dynamic and high-dimensional systems. Existing methods often struggle with efficiency and scalability. The authors propose LOCAL to mitigate these issues by employing a quasi-maximum likelihood-based score function and adaptive modules.

Key Contributions

1. Quasi-Maximum Likelihood-Based Objective: LOCAL introduces a quasi-likelihood approach to estimate dynamic causal structures. This method enhances the robustness and accuracy of causal inference compared to previous approaches that heavily rely on complex constraints and computationally expensive matrix operations.
2. Adaptive Modules for Improved Causal Discovery:
   • Asymptotic Causal Mask Learning (ACML): This module uses learnable priority vectors and the Gumbel-Sigmoid function to facilitate the efficient creation of DAGs, bypassing the need for hard constraints.
   • Dynamic Graph Parameter Learning (DGPL): This module breaks down causal learning into decomposed matrix multiplications, enhancing the interpretability of causal relationships in high-dimensional data.
3. Efficiency and Performance: The LOCAL framework demonstrates significant improvements in efficiency, requiring substantially less computational time while achieving superior accuracy on synthetic and real datasets.

Experimental Verification

The paper validates LOCAL's effectiveness through extensive experiments:

• Synthetic Data: LOCAL significantly outperforms traditional methods like DYNOTEARS and its extensions, especially as the dimensionality of the data increases. The experiments reveal considerable gains in True Positive Rate (TPR), Structural Hamming Distance (SHD), and F1 scores.
• NetSim and CausalTime Datasets: The method demonstrates strong performance in capturing complex nonlinear causal relationships, surpassing state-of-the-art methods in both AUROC and AUPRC metrics.

Implications and Future Work

The research indicates that LOCAL's innovative approach to architectural design and objective formulation allows for improved scalability and accuracy in dynamic causal discovery. This method can be pivotal for applications requiring efficient causal inference without the computational costs associated with traditional methods.

Future work may involve exploring additional neural architectures, such as attention-based mechanisms, to further enhance LOCAL's capabilities and extend its applicability to even more complex causal structures.

Conclusion

LOCAL presents a promising advancement in the field of causal discovery from time series data, offering a robust and efficient solution to longstanding challenges. Its integration of quasi-maximum likelihood estimation with novel adaptive modules establishes a new paradigm for rapid and accurate causal inference in high-dimensional dynamic systems.