# DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding

arXiv: https://arxiv.org/abs/2510.02117 · HTML: https://mlsanity.com/paper/2510.02117/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 16 of 16)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Ordering-Based Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1910.09014/) (2019)
- [Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors](https://mlsanity.com/paper/2207.01237/) (2022)
- [The DeCAMFounder: Non-Linear Causal Discovery in the Presence of Hidden Variables](https://mlsanity.com/paper/2102.07921/) (2021)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Markov Equivalence and Consistency in Differentiable Structure Learning](https://mlsanity.com/paper/2410.06163/) (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)

## Built on by (most cited first, 2 of 2)

- [Integrating Causal Inference with Graph Neural Networks for Alzheimer's Disease Analysis](https://mlsanity.com/paper/2511.14922/) (2025)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)

## Abstract (arXiv)

We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or nonlinearity. We propose textscDECOR, a single likelihood-based and fully differentiable estimator that jointly learns a DAG and a correlated noise model. Our theory gives simple sufficient conditions for global parameter identifiability: if the mixed graph is bow free and the noise covariance has a uniform eigenvalue margin, then the map from (B,OmegaMat) to the observational covariance is injective, so both the directed structure and the noise are uniquely determined. The estimator alternates a smooth-acyclic graph update with a convex noise update and can include a light bow complementarity penalty or a post hoc reconciliation step. On synthetic benchmarks that vary confounding density, graph density, latent rank, and dimension with n<p, textscDECOR matches or outperforms strong baselines and is especially robust when confounding is non-pervasive, while remaining competitive under pervasiveness.