# Causal Discovery with Unobserved Confounding and non-Gaussian Data

arXiv: https://arxiv.org/abs/2007.11131 · HTML: https://mlsanity.com/paper/2007.11131/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 25 of 25)

- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learning](https://mlsanity.com/paper/2303.12703/) (2023)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (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)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Causal Additive Models with Unobserved Causal Paths and Backdoor Paths](https://mlsanity.com/paper/2502.07646/) (2025)
- [Causal Discovery in Linear Structural Causal Models with Deterministic Relations](https://mlsanity.com/paper/2111.00341/) (2021)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Detecting and Measuring Confounding Using Causal Mechanism Shifts](https://mlsanity.com/paper/2409.17840/) (2024)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles](https://mlsanity.com/paper/2507.10767/) (2025)
- [Score-Based Causal Discovery of Latent Variable Causal Models](https://mlsanity.com/paper/2605.20396/) (2026)
- [Generalization of LiNGAM that allows confounding](https://mlsanity.com/paper/2401.16661/) (2024)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Algorithmic Identification of Essential Exogenous Nodes for Causal Sufficiency in Brain Networks](https://mlsanity.com/paper/2403.05407/) (2024)
- [Efficiently Deciding Algebraic Equivalence of Bow-Free Acyclic Path Diagrams](https://mlsanity.com/paper/2406.09049/) (2024)
- [Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables](https://mlsanity.com/paper/2606.08196/) (2026)
- [Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling](https://mlsanity.com/paper/2503.09194/) (2025)
- [Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences](https://mlsanity.com/paper/2511.10031/) (2025)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)
- [Causal discovery under mean independence and linearity](https://mlsanity.com/paper/2605.04381/) (2026)
- [Linear Regression Beyond Covariance: Latent Slope Spectra from Higher-Order Cumulants](https://mlsanity.com/paper/2610.17772/) (2026)

## Abstract (arXiv)

We consider recovering causal structure from multivariate observational data. We assume the data arise from a linear structural equation model (SEM) in which the idiosyncratic errors are allowed to be dependent in order to capture possible latent confounding. Each SEM can be represented by a graph where vertices represent observed variables, directed edges represent direct causal effects, and bidirected edges represent dependence among error terms. Specifically, we assume that the true model corresponds to a bow-free acyclic path diagram; i.e., a graph that has at most one edge between any pair of nodes and is acyclic in the directed part. We show that when the errors are non-Gaussian, the exact causal structure encoded by such a graph, and not merely an equivalence class, can be recovered from observational data. The method we propose for this purpose uses estimates of suitable moments, but, in contrast to previous results, does not require specifying the number of latent variables a priori. We also characterize the output of our procedure when the assumptions are violated and the true graph is acyclic, but not bow-free. We illustrate the effectiveness of our procedure in simulations and an application to an ecology data set.