Learning Temporal Causal Structure via Smooth Differentiable Optimization
通过平滑可微优化学习时间因果结构
Tong Zhao, Ce Guo, Wayne Luk, Emil Lupu, Ray Dipojjwal
AI总结 提出使用Gumbel-Sinkhorn算子学习可微变量排序,三角化结构向量自回归模型的瞬时系数矩阵,将无环性转化为参数化,实现统一连续优化,提高时间序列因果发现的效率和准确性。
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多变量时间序列中具有瞬时效应的因果发现具有挑战性,因为瞬时结构必须是无环的。先前的方法通过将瞬时和滞后估计分离为多阶段流水线,或通过复杂的增广拉格朗日优化施加代数无环性约束来强制执行这一点,这两种方法都 incur 高计算成本。在这项工作中,我们提出了一种不同的方法:我们使用Gumbel-Sinkhorn算子学习变量的可微排列,并按照学习到的顺序三角化结构向量自回归(SVAR)模型的瞬时系数矩阵。这将无环性从硬约束转化为参数化,并在整个优化过程中保持其有效性。通过这样做,我们的方法实现了基于梯度的学习的统一连续优化,从而提高了时间序列因果发现的效率。在三个真实世界基准测试中,我们的方法在发现准确性和效率方面均优于12个基线方法,取得了最佳整体性能。在大规模基准测试中,它进一步展示了强大的可扩展性,实现了比竞争方法快6倍以上的加速。
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.