Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders
Abstract
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 ≳ max{slog p, r p} samples. Experimental results validate our theoretical contributions.
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BibTeX
@misc{yu2026provable,
title = {{Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders}},
author = {Weijian Yu and Jean Honorio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18535},
eprint = {2609.18535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18535},
}
RIS
TY - UNPB
TI - Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders
AU - Weijian Yu
AU - Jean Honorio
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18535
UR - https://arxiv.org/abs/2609.18535
AB - 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 ≳ max{slog p, r p} samples. Experimental results validate our theoretical contributions.
ER -