# Parameter identification in linear non-Gaussian causal models under general confounding

arXiv: https://arxiv.org/abs/2405.20856 · HTML: https://mlsanity.com/paper/2405.20856/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 85 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 18 of 18)

- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [Maximum Flow and Minimum-Cost Flow in Almost-Linear Time](https://mlsanity.com/paper/2203.00671/) (2022)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [A Cross-Moment Approach for Causal Effect Estimation](https://mlsanity.com/paper/2306.06263/) (2023)
- [When does the ID algorithm fail?](https://mlsanity.com/paper/2307.03750/) (2023)
- [Learning Linear Non-Gaussian Graphical Models with Multidirected Edges](https://mlsanity.com/paper/2010.05306/) (2020)
- [The Hellinger Correlation](https://mlsanity.com/paper/1810.10276/) (2018)
- [On Identifiability of Conditional Causal Effects](https://mlsanity.com/paper/2306.11755/) (2023)
- [Goodness-of-Fit Tests for Linear Non-Gaussian Structural Equation Models](https://mlsanity.com/paper/2311.04585/) (2023)
- [Non-Independent Components Analysis](https://mlsanity.com/paper/2206.13668/) (2022)
- [The multidimensional truncated Moment Problem: The Moment Cone](https://mlsanity.com/paper/1809.00584/) (2018)

## Built on by (most cited first, 5 of 5)

- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [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)
- [A PC Algorithm for Max-Linear Bayesian Networks](https://mlsanity.com/paper/2508.13967/) (2025)
- [Linear Causal Representation Learning by Topological Ordering, Pruning, and Disentanglement](https://mlsanity.com/paper/2509.22553/) (2025)

## Abstract (arXiv)

Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent variables. Our focus is on the commonly studied acyclic setting, where each model corresponds to a directed acyclic graph (DAG). For this case, prior literature has demonstrated that connections to overcomplete independent component analysis yield effective criteria to decide parameter identifiability in latent variable models. However, this connection is based on the assumption that the observed variables linearly depend on the latent variables. Departing from this assumption, we treat models that allow for arbitrary non-linear latent confounding. Our main result is a graphical criterion that is necessary and sufficient for deciding the generic identifiability of direct causal effects. Moreover, we provide an algorithmic implementation of the criterion with a run time that is polynomial in the number of observed variables. Finally, we report on estimation heuristics based on the identification result and explore a generalization to models with feedback loops.