# Causal Discovery in Linear Models with Unobserved Variables and Measurement Error

arXiv: https://arxiv.org/abs/2407.19426 · HTML: https://mlsanity.com/paper/2407.19426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 28 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Anchored Causal Inference in the Presence of Measurement Error](https://mlsanity.com/paper/1906.00928/) (2019)
- [Anchored Discrete Factor Analysis](https://mlsanity.com/paper/1511.03299/) (2015)
- [A Cross-Moment Approach for Causal Effect Estimation](https://mlsanity.com/paper/2306.06263/) (2023)
- [Causal Discovery in Linear Latent Variable Models Subject to Measurement Error](https://mlsanity.com/paper/2211.03984/) (2022)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Generalized Independent Noise Condition for Estimating Latent Variable Causal Graphs](https://mlsanity.com/paper/2010.04917/) (2020)
- [Multiscale Blind Source Separation](https://mlsanity.com/paper/1608.07173/) (2016)

## Built on by (most cited first, 1 of 1)

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)

## Abstract (arXiv)

The presence of unobserved common causes and measurement error poses two major obstacles to causal structure learning, since ignoring either source of complexity can induce spurious causal relations among variables of interest. We study causal structure learning in linear systems where both challenges may occur simultaneously. We introduce a causal model called LV-SEM-ME, which contains four types of variables: directly observed variables, variables that are not directly observed but are measured with error, the corresponding measurements, and variables that are neither observed nor measured. Under a separability condition-namely, identifiability of the mixing matrix associated with the exogenous noise terms of the observed variables-together with certain faithfulness assumptions, we characterize the extent of identifiability and the corresponding observational equivalence classes. We provide graphical characterizations of these equivalence classes and develop recovery algorithms that enumerate all models in the equivalence class of the ground truth. We also establish, via a four-node union model that subsumes instrumental variable, front-door, and negative-control-outcome settings, a form of identification robustness: the target effect remains identifiable in the broader LV-SEM-ME model even when the assumptions underlying the specialized identification formulas for the corresponding submodels need not all hold simultaneously.