# High-Dimensional Causal Discovery Under non-Gaussianity

arXiv: https://arxiv.org/abs/1803.11273 · HTML: https://mlsanity.com/paper/1803.11273/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2018.

## Built on by (most cited first, 24 of 24)

- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Unpaired Multi-Domain Causal Representation Learning](https://mlsanity.com/paper/2302.00993/) (2023)
- [Optimal estimation of Gaussian DAG models](https://mlsanity.com/paper/2201.10548/) (2022)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Learning for Counterfactual Fairness from Observational Data](https://mlsanity.com/paper/2307.08232/) (2023)
- [Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants](https://mlsanity.com/paper/2312.11934/) (2023)
- [Learning Linear Non-Gaussian Polytree Models](https://mlsanity.com/paper/2208.06701/) (2022)
- [Learning linear non-Gaussian directed acyclic graph with diverging number of nodes](https://mlsanity.com/paper/2111.00740/) (2021)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores](https://mlsanity.com/paper/2202.01748/) (2022)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles](https://mlsanity.com/paper/2507.10767/) (2025)
- [Learning causal graphs using variable grouping according to ancestral relationship](https://mlsanity.com/paper/2403.14125/) (2024)
- [Learning Directed Acyclic Graphs from Partial Orderings](https://mlsanity.com/paper/2403.16031/) (2024)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers](https://mlsanity.com/paper/2111.01560/) (2021)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [Linear causal disentanglement via higher-order cumulants](https://mlsanity.com/paper/2407.04605/) (2024)
- [Structural transfer learning of non-Gaussian DAG](https://mlsanity.com/paper/2310.10239/) (2023)
- [A PC Algorithm for Max-Linear Bayesian Networks](https://mlsanity.com/paper/2508.13967/) (2025)
- [Causal discovery under mean independence and linearity](https://mlsanity.com/paper/2605.04381/) (2026)
- [MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimization](https://mlsanity.com/paper/2609.30643/) (2026)

## Abstract (arXiv)

We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, σ, of the variables such that each observed variable Yv is a linear function of a variable specific error term and the other observed variables Yu with σ(u) < σ (v). The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has been previously shown that when the variable specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.