Causal discovery under a confounder blanket
This work addresses a specialized but important problem for researchers in fields like biomolecular studies, where genetic data provides background information, offering a tractable approach for high-dimensional causal inference.
The paper tackles the problem of causal discovery in high-dimensional observational data by focusing on recovering causal order among a subset of variables influenced by a set of confounding covariates, known as a confounder blanket, and presents a method that accommodates varying graph sparsity with polynomial time complexity, demonstrating it on simulated and real-world datasets.
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 the causal order among a subgraph of variables known to descend 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 background information. Under a structural assumption called the $\textit{confounder blanket principle}$, which we argue is essential for tractable causal discovery in high dimensions, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We present a structure learning algorithm that is provably sound and complete with respect to a so-called $\textit{lazy oracle}$. We design inference procedures with finite sample error control for linear and nonlinear systems, and demonstrate our approach on a range of simulated and real-world datasets. An accompanying $\texttt{R}$ package, $\texttt{cbl}$, is available from $\texttt{CRAN}$.