🤖 AI Summary
This work addresses a key limitation in existing time series causal discovery methods, which typically assume a fixed lag order and thus struggle to capture variable-lag dependencies. The authors propose a Tabu search–based structure learning algorithm that independently optimizes the lag order for each causal edge while respecting temporal ordering constraints. By introducing a decomposable BIC scoring function that incorporates both effective sample size per node and a penalty for lag length, the method guarantees local optimality in theory and supports parallelization for improved scalability. Experiments demonstrate that the approach accurately recovers graph structures and precisely estimates lags in synthetic data. When applied to UK COVID-19 policy data, it identifies causal relationships dominated by short lags yet also exhibiting longer-lag effects, aligning well with established epidemiological principles.
📝 Abstract
Causal Bayesian Networks (CBNs) are a powerful tool for reasoning under uncertainty about complex real-world problems. Such problems evolve over time, responding to external shocks as they occur. To support decision-making, CBNs require a cause-and-effect map of the variables under consideration, known as the network's structure. Learning the graphical structure of a causal model from data remains challenging; learning it from time-series data is even harder because dependencies may arise at different time lags. Existing time-series causal discovery methods often assume a fixed lag window and do not explicitly optimise edge-specific lags. We propose a Tabu-based structure learning algorithm that searches for a time-ordered directed structure (i.e., where every edge respects time) while allowing edge-specific lags up to a specified maximum lag. The approach uses a decomposable BIC-based score with node-specific effective sample sizes and an explicit lag-length penalty encouraging parsimonious delay assignments while preserving efficient local score updates. We provide theoretical guarantees of validity and local optimality, and we also describe a parallel implementation for improved scalability. In simulations, the method recovered graph structure competitively and estimated lags accurately when true adjacencies were recovered. On a real-world UK COVID-19 policy dataset, the learnt structure was dominated by short delays while retaining a substantial minority of longer-lag dependencies, consistent with delayed behavioural and epidemiological effects.