# Causal discovery under a confounder blanket

arXiv: https://arxiv.org/abs/2205.05715 · HTML: https://mlsanity.com/paper/2205.05715/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 55 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 3 of 3)

- [Panning for Gold: Model-X Knockoffs for High-dimensional Controlled Variable Selection](https://mlsanity.com/paper/1610.02351/) (2016)
- [Ancestral Causal Inference](https://mlsanity.com/paper/1606.07035/) (2016)
- [A Weaker Faithfulness Assumption based on Triple Interactions](https://mlsanity.com/paper/2010.14265/) (2020)

## Built on by (most cited first, 6 of 6)

- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [Local Causal Discovery for Statistically Efficient Causal Inference](https://mlsanity.com/paper/2510.14582/) (2025)
- [Multi-omic Causal Discovery using Genotypes and Gene Expression](https://mlsanity.com/paper/2505.15866/) (2025)
- [Causal ASCEND: Scalable Two-tier Causal Discovery on High Dimensional Multi-omics Data](https://mlsanity.com/paper/2607.04527/) (2026)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

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 textitconfounder 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 textitconfounder 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 textitlazy 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 textttR package, textttcbl, is available from textttCRAN.