Structure Learning from Time-Series Data with Lag-Agnostic Structural Prior

Learning instantaneous and time-lagged causal relationships from time-series data is essential for uncovering fine-grained, temporally-aware interactions. Although this problem has been formulated as a continuous optimization task amenable to modern machine learning methods, the integration of coarse-grained lag-agnostic causal priors, an important and commonly available form of prior knowledge, remains largely unaddressed. To address this gap, we propose a novel framework for structure learning from time series to integrate lag-agnostic priors, enabling the discovery of lag-specific causal links without requiring precise information on the exact lag of causality. We introduce formulations to precisely characterize the lag-agnostic priors, and demonstrate their consequential and process-equivalence to priors, maintaining consistency with the intended semantics of the priors throughout optimization. We further analyze the challenge for optimization due to the increased non-convexity by lag-agnostic prior constraints, and introduce a datadriven initialization to mitigate this issue. Experiments on both synthetic and real-world datasets show that our method effectively incorporates lag-agnostic prior knowledge to enhance the recovery of fine-grained, lag-aware structures.