Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or extreme sparsity constraints. We relax these assumptions and focus on an important but more specialized problem, namely recovering a directed acyclic subgraph of variables known to be causally descended from some (possibly large) set of confounding covariates, i.e. a $\textit{confounder blanket}$. This is useful in many settings, for example when studying a dynamic biomolecular subsystem with genetic data providing causally relevant background information. Under a structural assumption that, we argue, must be satisfied in practice if informative answers are to be found, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We derive a sound and complete algorithm for identifying causal relationships under these conditions and implement testing procedures with provable error control for linear and nonlinear systems. We demonstrate our approach on a range of simulation settings.

本研究提出一种名为“混淆毯原则”的结构假设，使得我们设计的因果关系推断算法能够适用于高维数据，同时保持多项式复杂度。我们演示了我们的方法在模拟和真实数据集上的运作，包括一个用于线性和非线性系统的推断过程和有限样本误差控制。

混淆变量下的因果发现