提出因果效应符号可识别性，突破传统模型假设限制。
Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems
- 不依赖已知扩散矩阵，基于观测协方差矩阵判断因果边符号
- 发现三类可识别性：可识别、不可识别、部分可识别
- 适用于经典与新型循环结构，可推导目标边符号表达式
我们研究具有已知因果结构的连续时间线性平稳随机微分方程中的可识别性问题。不同于现有方法，我们放宽了对已知扩散矩阵的假设，尊重模型的内在尺度不变性。因此，不再恢复漂移系数本身，而是引入边符号可识别性：在给定因果结构下，判断某漂移项符号是否在所有与该结构兼容的参数化所诱导的观测协方差矩阵中唯一确定。这导致了边符号可识别性的三分类：可识别、不可识别、部分可识别。这一三分类引入了新的部分可识别概念，我们证明其在本设置中是真实存在的类别。在一种忠实性假设下，我们推导出一般图中各类别的判定准则。将这些准则应用于具体因果结构，包括类似经典因果设置（如工具变量）和新型循环设置，我们确定了它们的边符号可识别性，并在某些情况下得到了目标边符号关于观测协方差矩阵的显式表达式。
原文摘要 · Abstract (English)
We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Therefore, rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrisations compatible with that structure. This leads to a trichotomy of edge-sign identifiability: identifiable, non-identifiable, and partially identifiable. This trichotomy introduces the new notion of partial identifiability to the literature, which we show is a genuine category in our setting. Under a notion of faithfulness, we derive criteria to identify membership of each category for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix.
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