提出非对称独立性模型，实现路径空间中因果发现的统一理论框架。
An Asymmetric Independence Model for Causal Discovery on Path Spaces
- 基于随机微分方程建立因果依赖的图模型，用变量进入对方方程来定义因果关系。
- 证明循环系统存在全局马尔可夫性质，且在部分观测下仍保持独立性闭包。
- 给出等价图类的最大表示元，适用于数据驱动的因果结构推断与复杂系统分析。
我们建立了有向混合图（DMGs）中的'E-分离'与随机微分方程（SDEs）坐标过程间条件独立关系之间的理论联系，其中因果关系由'哪些变量进入其他变量的控制方程'决定。我们证明了循环SDEs的全局马尔可夫性质，并自然扩展到部分可观测的循环SDEs，因为我们的非对称独立性模型在边缘化下是封闭的。随后，我们刻画了编码相同独立性关系的图类，得到一个类似于经典有向无环图（DAGs）中'同骨架且同v-结构'的重要结果。在完全观测情况下，我们证明每个等价类图均有最大元素作为简洁表示，并开发了从数据中识别该最大元素的算法。我们推测在部分观测下同样存在最大元素，并通过计算验证了最多四节点图的情况。
原文摘要 · Abstract (English)
We develop the theory linking 'E-separation' in directed mixed graphs (DMGs) with conditional independence relations among coordinate processes in stochastic differential equations (SDEs), where causal relationships are determined by "which variables enter the governing equation of which other variables". We prove a global Markov property for cyclic SDEs, which naturally extends to partially observed cyclic SDEs, because our asymmetric independence model is closed under marginalization. We then characterize the class of graphs that encode the same set of independence relations, yielding a result analogous to the seminal 'same skeleton and v-structures' result for directed acyclic graphs (DAGs). In the fully observed case, we show that each such equivalence class of graphs has a greatest element as a parsimonious representation and develop algorithms to identify this greatest element from data. We conjecture that a greatest element also exists under partial observations, which we verify computationally for graphs with up to four nodes.
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