# Robust causal structure learning with some hidden variables

arXiv: https://arxiv.org/abs/1708.01151 · HTML: https://mlsanity.com/paper/1708.01151/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2017.

## Built on by (most cited first, 17 of 17)

- [Learning latent causal graphs via mixture oracles](https://mlsanity.com/paper/2106.15563/) (2021)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Identifying Weight-Variant Latent Causal Models](https://mlsanity.com/paper/2208.14153/) (2022)
- [Identifiable Latent Polynomial Causal Models Through the Lens of Change](https://mlsanity.com/paper/2310.15580/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Causal Effect Variational Autoencoder with Uniform Treatment](https://mlsanity.com/paper/2111.08656/) (2021)
- [Towards Identifiable Latent Additive Noise Models](https://mlsanity.com/paper/2403.15711/) (2024)
- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)
- [Identification of Latent Variables From Graphical Model Residuals](https://mlsanity.com/paper/2101.02332/) (2021)
- [On Theoretical Identifiability of Discrete Latent Causal Graphical Models](https://mlsanity.com/paper/2505.18410/) (2025)
- [From 'What-is' to 'What-if' in Human-Factor Analysis: A Post-Occupancy Evaluation Case](https://mlsanity.com/paper/2512.02060/) (2025)
- [Causal Discovery with Mixed Latent Confounding via Precision Decomposition](https://mlsanity.com/paper/2512.24696/) (2025)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)
- [LUCID: Learning Under Confounding for Inference and Discovery in Time Series](https://mlsanity.com/paper/2609.31315/) (2026)

## Abstract (arXiv)

We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed ones. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables, and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high-dimensional regimes and performs favourably when compared to the state of the art, both in terms of graphical structure recovery and total causal effect estimation.