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.

翻译：从时间序列观测数据中发现底层有向无环图（DAG）极具挑战性，这源于变量的动态特性及复杂的非线性交互作用。现有方法常受限于效率低下及对高维数据的处理能力。为弥补这一研究空白，我们提出了LOCAL——一种高效、易于实现且无约束的动态因果结构恢复方法。LOCAL首次尝试构建一种基于拟极大似然的评分函数，用于学习与真实情况等价的动态DAG。在此基础上，我们提出了两个自适应模块，通过新功能增强无环性的代数表征：渐近因果掩码学习（ACML）与动态图参数学习（DGPL）。ACML利用可学习的优先级向量和Gumbel-Sigmoid函数生成因果掩码，在优化计算效率的同时确保生成DAG。DGPL将因果学习转化为分解矩阵乘积，以捕捉高维数据的动态因果结构并提升可解释性。在合成数据集和真实数据集上的大量实验表明，LOCAL显著优于现有方法，并凸显了其作为动态因果发现的鲁棒高效方法的潜力。我们的代码即将公开。