用可微排列方法高效发现多变量时间序列的因果结构。
Learning Temporal Causal Structure via Smooth Differentiable Optimization
- 用Gumbel-Sinkhorn算子学习变量顺序，三角化瞬时系数矩阵。
- 在三个真实数据集上优于12种基线，大尺度数据快6倍以上。
- 适合需要高效因果发现的工业级时间序列分析场景。
多变量时间序列中的瞬时因果发现面临挑战，因瞬时结构必须无环。现有方法通过分阶段估计或复杂对偶拉格朗日优化施加代数无环约束，计算成本高。本文提出新方法：利用Gumbel-Sinkhorn算子学习变量的可微排列，并按此顺序三角化结构向量自回归（SVAR）模型的瞬时系数矩阵，将无环性从硬约束转为参数化，全程保持有效。该方法实现统一连续优化与梯度学习，显著提升效率。在三个真实世界基准测试中，本方法在因果发现准确率和效率上均优于12种基线；在大规模基准上更展现强可扩展性，较竞争方法提速超6倍。
原文摘要 · Abstract (English)
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.
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