GRACE: Gated Refinement for Accurate Causal Edge Discovery in High-Dimensional Time Series

Inferring causal relationships from multivariate time series is a fundamental challenge in fields like climate science and genomics. Existing methods face a trade-off: constraint-based approaches are statistically rigorous but computationally expensive at high dimensions, while score-based and attention-based methods are faster but often struggle with binarizing continuous edge scores, leading to poor precision or reliance on arbitrary thresholds.

The authors propose GRACE (Gated Refinement for Accurate Causal Edge discovery), a two-stage framework. First, a high-recall constraint-based method (such as CDNOTS or PCMCI) generates a candidate skeleton of potential causal edges. Second, a gated neural model refines this skeleton. Each candidate edge is assigned an independent Hard Concrete gate trained with L0 regularization. This mechanism forces gate values to concentrate near 0 or 1, creating a clear bimodal distribution that allows for a robust binary decision at a 0.5 threshold, effectively pruning false positives while retaining true causal links.

GRACE consistently outperforms existing baselines across diverse synthetic benchmarks. At high dimensionality (d=100), it maintains high precision and recall, achieving significantly higher F1 scores than state-of-the-art score-based and attention-based methods. Notably, GRACE achieves performance comparable to expensive nonlinear conditional independence tests while being approximately 75 times faster. In a real-world application involving the Elbe River, the method successfully recovered 9 of 11 causal edges while reducing the skeleton's false positive count by 99%.

By decoupling the initial discovery of candidate edges from the final refinement of the causal graph, GRACE provides a scalable and robust solution for high-dimensional causal inference. The use of Hard Concrete gates with L0 regularization removes the need for dataset-specific threshold tuning, making the method more reliable for practitioners working with complex, real-world datasets where causal structures are unknown.