Causal Structural Learning from Time Series: A Convex Optimization Approach
This work addresses a foundational challenge in causal reasoning and scientific discovery by enabling more efficient and reliable structural learning from time series data, representing an incremental improvement through the application of convex optimization techniques.
The paper tackled the non-convex problem of learning directed acyclic graphs (DAGs) from time series data by proposing a data-adaptive linear approach that can be cast into a convex optimization problem using a monotone operator variational inequality formulation, and it showed superior performance in structure recovery over existing methods in numerical experiments.
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.