# Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders

arXiv: https://arxiv.org/abs/2609.18535 · HTML: https://mlsanity.com/paper/2609.18535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 16 Sep 2026.

## Builds on (most cited first, 6 of 6)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Learning Latent Variable Gaussian Graphical Models](https://mlsanity.com/paper/1406.2721/) (2014)
- [Score-Based Causal Discovery of Latent Variable Causal Models](https://mlsanity.com/paper/2605.20396/) (2026)

## Abstract (arXiv)

Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for p observed variables, r latent confounders and s edges, our procedure correctly identifies the directed causal relationship among observed variables, for n gtrsim maxslog p, r p samples. Experimental results validate our theoretical contributions.