Learning Temporal Causal Structure via Smooth Differentiable Optimization
This work addresses the computational bottleneck in causal discovery for multivariate time series, offering a more efficient and accurate approach for practitioners.
The authors propose a differentiable method for learning temporal causal structure that replaces the acyclicity constraint with a parameterization using the Gumbel-Sinkhorn operator, enabling unified gradient-based optimization. On three real-world benchmarks, their method achieves the best overall accuracy and efficiency, with over 6x speedup on large-scale data.
Causal discovery with instantaneous effects in multivariate time series is challenging, as the instantaneous structure must be acyclic. Prior methods enforce this by either separating instantaneous and lagged estimation into multi-stage pipelines or imposing algebraic acyclicity constraints via complex augmented Lagrangian optimization, both of which incur high computational cost. In this work, we propose a different approach: we learn a differentiable permutation of variables using the Gumbel--Sinkhorn operator and triangularize the instantaneous coefficient matrix of a Structural Vector Autoregressive (SVAR) model in the learned order. This converts acyclicity from a hard constraint into a parameterization and keeps it valid throughout optimization. In doing so, our method enables unified, continuous optimization with gradient-based learning, leading to improved efficiency in time--series causal discovery. Across three real-world benchmarks, our method achieves the best overall performance compared with 12 baselines in both discovery accuracy and efficiency. On the large-scale benchmark, it further demonstrates strong scalability, achieving more than a 6x speedup over competing methods.