提出可微分因果发现框架，同时识别时序与瞬时因果关系。
SC3D: Dynamic and Differentiable Causal Discovery for Temporal and Instantaneous Graphs
- 两阶段可微框架，先预选边再优化稀疏性与无环性
- 在合成与真实数据上均优于现有方法，恢复更准确
- 适合处理含时滞与瞬时依赖的复杂动态图结构
从多变量时间序列中发现因果结构是关键问题，因为交互涉及多个时滞并可能包含瞬时依赖。此外，动态图的搜索空间具有组合性质。本文提出稳定因果动态可微发现（SC3D），一种两阶段可微框架，联合学习滞后特定邻接矩阵及若存在则学习瞬时有向无环图（DAG）。第一阶段通过节点级预测进行边预选，获取滞后与瞬时边的掩码；第二阶段通过优化似然函数，结合稀疏性约束，并在瞬时块上强制无环性来精炼这些掩码。在合成SVAR系统、非线性与混沌基准、非平稳动态及真实数据集上的数值结果表明，相较于现有基线，SC3D在稳定性与滞后及瞬时因果结构恢复准确性方面均有提升。
原文摘要 · Abstract (English)
Discovering causal structures from multivariate time series is a key problem because interactions span across multiple lags and possibly involve instantaneous dependencies. Additionally, the search space of the dynamic graphs is combinatorial in nature. In this study, we propose Stable Causal Dynamic Differentiable Discovery (SC3D), a two-stage differentiable framework that jointly learns lag-specific adjacency matrices and, if present, an instantaneous directed acyclic graph (DAG). In Stage 1, SC3D performs edge preselection through node-wise prediction to obtain masks for lagged and instantaneous edges, whereas Stage 2 refines these masks by optimizing a likelihood with sparsity along with enforcing acyclicity on the instantaneous block. Numerical results across synthetic SVAR systems, nonlinear and chaotic benchmarks, nonstationary dynamics and real-world datasets demonstrate that SC3D achieves improved stability and more accurate recovery of both lagged and instantaneous causal structures compared to existing baselines.
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