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 often struggle with inefficiency and the handling of high-dimensional data. To address these research gap, 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. On this basis, we propose two adaptive modules for enhancing the algebraic characterization of acyclicity with new capabilities: Asymptotic Causal Mask Learning (ACML) and Dynamic Graph Parameter Learning (DGPL). ACML generates causal masks using learnable priority vectors and the Gumbel-Sigmoid function, ensuring the creation of DAGs while optimizing computational efficiency. DGPL transforms causal learning into decomposed matrix products, capturing the dynamic causal structure of high-dimensional data and enhancing 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. Our code will be available soon.

该研究针对从时间序列观测数据中发现潜在有向无环图（DAG）的难题，提出了新方法LOCAL。通过引入准最大似然评分函数和两种适应性模块，LOCAL在捕捉动态因果结构和提高计算效率方面具有显著优势，实验结果表明其性能优于现有方法。

LOCAL：利用方向矩阵从时间序列数据推断因果结构的学习