# Causal Discovery in the Presence of Measurement Error: Identifiability Conditions

arXiv: https://arxiv.org/abs/1706.03768 · HTML: https://mlsanity.com/paper/1706.03768/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2017.

## Built on by (most cited first, 9 of 9)

- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Assumption violations in causal discovery and the robustness of score matching](https://mlsanity.com/paper/2310.13387/) (2023)
- [Causal Graph Discovery with Retrieval-Augmented Generation based Large Language Models](https://mlsanity.com/paper/2402.15301/) (2024)
- [Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Models](https://mlsanity.com/paper/2210.11021/) (2022)
- [Causal Discovery from Conditionally Stationary Time Series](https://mlsanity.com/paper/2110.06257/) (2021)
- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)
- [Improved Bound for Robust Causal Bandits with Linear Models](https://mlsanity.com/paper/2405.07795/) (2024)

## Abstract (arXiv)

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model for the measurement-error-free variables can be identified in the presence of measurement error with unknown variance. In this paper, we study precise sufficient identifiability conditions for the measurement-error-free causal model and show what information of the causal model can be recovered from observed data. In particular, we present two different sets of identifiability conditions, based on the second-order statistics and higher-order statistics of the data, respectively. The former was inspired by the relationship between the generating model of the measurement-error-contaminated data and the factor analysis model, and the latter makes use of the identifiability result of the over-complete independent component analysis problem.