仅需两个噪声不同的环境数据，即可唯一确定因果图。
On the Identifiability of Causal Graphs with the Invariance Principle
- 利用噪声统计差异的不变性原理识别因果结构
- 仅需2个环境即可完全恢复因果图，且适用于任意非线性机制
- 适合从事因果推断与多源数据建模的研究者
从独立同分布的观测数据中进行因果发现通常为病态问题。本文证明：若已知结构因果模型诱导的分布，并额外获得（理想情况下）仅两个在噪声统计上显著不同的环境的数据，即可唯一识别出完整的因果图。这是文献中首个在固定数量环境和任意非线性机制下保证整个因果图可识别的结果。唯一约束是噪声项服从高斯分布；但本文也提出了放松该假设的潜在途径。此外，我们拓展了独立成分分析（ICA）与因果发现之间的经典对偶关系：近期研究表明，多环境下的非线性 ICA 可通过不少于源变量数的环境求解；而本文表明，在获取远少于源变量数的辅助信息条件下，因果发现同样可实现。
原文摘要 · Abstract (English)
Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution {induced} by a structural causal model, and additional data from (in the best case) \textit{only two} environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.
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