Causal discovery under a confounder blanket

TL;DR

This paper introduces a new causal discovery method that effectively infers causal order among variables influenced by confounders, especially in high-dimensional settings, without requiring restrictive assumptions.

Contribution

It proposes a novel algorithm under the confounder blanket principle that is provably sound, complete, and applicable to both sparse and dense graphs in high dimensions.

Findings

Algorithm is provably sound and complete.

Effective in high-dimensional, nonlinear, and linear systems.

Demonstrated on simulated and real datasets.

Abstract

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 $\texttt{CRAN}$.