# Causal Discovery with Mixed Latent Confounding via Precision Decomposition

arXiv: https://arxiv.org/abs/2512.24696 · HTML: https://mlsanity.com/paper/2512.24696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 31 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Differentiable Causal Discovery Under Unmeasured Confounding](https://mlsanity.com/paper/2010.06978/) (2020)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [Robust causal structure learning with some hidden variables](https://mlsanity.com/paper/1708.01151/) (2017)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Penalized FCI for Causal Structure Learning in a Sparse DAG for Biomarker Discovery in Parkinson's Disease](https://mlsanity.com/paper/2507.00173/) (2025)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding](https://mlsanity.com/paper/2510.02117/) (2025)

## Abstract (arXiv)

We study causal discovery from observational data in linear Gaussian systems affected by mixed latent confounding, where some unobserved factors act broadly across many variables while others influence only small subsets. This setting is common in practice and poses a challenge for existing methods: differentiable and score-based DAG learners can misinterpret global latent effects as causal edges, while latent-variable graphical models recover only undirected structure. We propose textscDCL-DECOR, a modular, precision-led pipeline that separates these roles. The method first isolates pervasive latent effects by decomposing the observed precision matrix into a structured component and a low-rank component. The structured component corresponds to the conditional distribution after accounting for pervasive confounders and retains only local dependence induced by the causal graph and localized confounding. A correlated-noise DAG learner is then applied to this deconfounded representation to recover directed edges while modeling remaining structured error correlations, followed by a simple reconciliation step to enforce bow-freeness. We provide identifiability results that characterize the recoverable causal target under mixed confounding and show how the overall problem reduces to well-studied subproblems with modular guarantees. Synthetic experiments that vary the strength and dimensionality of pervasive confounding demonstrate consistent improvements in directed edge recovery over applying correlated-noise DAG learning directly to the confounded data.