# On the Parameter Identifiability of Partially Observed Linear Causal Models

arXiv: https://arxiv.org/abs/2407.16975 · HTML: https://mlsanity.com/paper/2407.16975/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 61 references that are in the map.
- First posted on arXiv 24 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [Graphical continuous Lyapunov models](https://mlsanity.com/paper/2005.10483/) (2020)
- [Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models](https://mlsanity.com/paper/2302.13220/) (2023)

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

- [Latent Variable Causal Discovery under Selection Bias](https://mlsanity.com/paper/2512.11219/) (2025)
- [Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data](https://mlsanity.com/paper/2501.18990/) (2025)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [A Sample Efficient Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2506.08747/) (2025)
- [Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing](https://mlsanity.com/paper/2604.13218/) (2026)
- [Trek-Based Parameter Identification for Linear Causal Models With Arbitrarily Structured Latent Variables](https://mlsanity.com/paper/2507.18170/) (2025)
- [Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models](https://mlsanity.com/paper/2605.04413/) (2026)

## Abstract (arXiv)

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether the edge coefficients can be recovered given the causal structure and partially observed data. Our setting is more general than that of prior research - we allow all variables, including both observed and latent ones, to be flexibly related, and we consider the coefficients of all edges, whereas most existing works focus only on the edges between observed variables. Theoretically, we identify three types of indeterminacy for the parameters in partially observed linear causal models. We then provide graphical conditions that are sufficient for all parameters to be identifiable and show that some of them are provably necessary. Methodologically, we propose a novel likelihood-based parameter estimation method that addresses the variance indeterminacy of latent variables in a specific way and can asymptotically recover the underlying parameters up to trivial indeterminacy. Empirical studies on both synthetic and real-world datasets validate our identifiability theory and the effectiveness of the proposed method in the finite-sample regime. Code: https://github.com/dongxinshuai/scm-identify.