Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization problem; however, DAG learning remains a highly non-convex problem, and there has not been much work on leveraging well-developed convex optimization techniques for causal structural learning. We fill this gap by proposing a data-adaptive linear approach for causal structural learning from time series data, which can be conveniently cast into a convex optimization problem using a recently developed monotone operator variational inequality (VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee of the VI-based approach and show the superior performance of our proposed method on structure recovery over existing methods via extensive numerical experiments.

翻译：结构学习旨在从观测数据中学习有向无环图（Directed Acyclic Graphs, DAGs），是因果推理和科学发现的基础。近期研究将结构学习转化为连续优化问题；然而，DAG学习仍是一个高度非凸的问题，目前鲜有工作利用成熟的凸优化技术进行因果结构学习。我们提出了一种数据自适应的线性方法，用于从时间序列数据中学习因果结构，该方法可借助近期发展的单调算子变分不等式（Variational Inequality, VI）表述，方便地转化为凸优化问题。此外，我们建立了基于VI方法的非渐近恢复保证，并通过大量数值实验证明，所提方法在结构恢复性能上优于现有方法。