# Causal Discovery in Linear Latent Variable Models Subject to Measurement Error

arXiv: https://arxiv.org/abs/2211.03984 · HTML: https://mlsanity.com/paper/2211.03984/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [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)
- [FRITL: A Hybrid Method for Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2103.14238/) (2021)
- [Generalized Independent Noise Condition for Estimating Latent Variable Causal Graphs](https://mlsanity.com/paper/2010.04917/) (2020)
- [Causal Discovery in Linear Structural Causal Models with Deterministic Relations](https://mlsanity.com/paper/2111.00341/) (2021)
- [Multiscale Blind Source Separation](https://mlsanity.com/paper/1608.07173/) (2016)

## Built on by (most cited first, 7 of 7)

- [Learning Unknown Intervention Targets in Structural Causal Models from Heterogeneous Data](https://mlsanity.com/paper/2312.06091/) (2023)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Neuro-Causal Factor Analysis](https://mlsanity.com/paper/2305.19802/) (2023)
- [Towards Characterizing Domain Counterfactuals For Invertible Latent Causal Models](https://mlsanity.com/paper/2306.11281/) (2023)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [Causal Discovery in Linear Models with Unobserved Variables and Measurement Error](https://mlsanity.com/paper/2407.19426/) (2024)

## Abstract (arXiv)

We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.