# Causal Structure Discovery between Clusters of Nodes Induced by Latent Factors

arXiv: https://arxiv.org/abs/2207.01237 · HTML: https://mlsanity.com/paper/2207.01237/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2022.

## Built on by (most cited first, 18 of 18)

- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Standardizing Structural Causal Models](https://mlsanity.com/paper/2406.11601/) (2024)
- [Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery](https://mlsanity.com/paper/2503.17037/) (2025)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [How to Enhance Causal Discrimination of Utterances: A Case on Affective Reasoning](https://mlsanity.com/paper/2305.02615/) (2023)
- [DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding](https://mlsanity.com/paper/2510.02117/) (2025)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [A Review and Roadmap of Deep Causal Model from Different Causal Structures and Representations](https://mlsanity.com/paper/2311.00923/) (2023)
- [Working Paper: Active Causal Structure Learning with Latent Variables: Towards Learning to Detour in Autonomous Robots](https://mlsanity.com/paper/2410.20894/) (2024)
- [Towards Causal Representation Learning and Deconfounding from Indefinite Data](https://mlsanity.com/paper/2305.02640/) (2023)
- [Towards Causal Relationship in Indefinite Data: Baseline Model and New Datasets](https://mlsanity.com/paper/2401.08221/) (2024)
- [Relaxed Sparsest-Permutation Formulation for Causal Discovery at Scale](https://mlsanity.com/paper/2605.05568/) (2026)
- [A Recursive Decomposition Framework for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2605.10651/) (2026)

## Abstract (arXiv)

We consider the problem of learning the structure of a causal directed acyclic graph (DAG) model in the presence of latent variables. We define latent factor causal models (LFCMs) as a restriction on causal DAG models with latent variables, which are composed of clusters of observed variables that share the same latent parent and connections between these clusters given by edges pointing from the observed variables to latent variables. LFCMs are motivated by gene regulatory networks, where regulatory edges, corresponding to transcription factors, connect spatially clustered genes. We show identifiability results on this model and design a consistent three-stage algorithm that discovers clusters of observed nodes, a partial ordering over clusters, and finally, the entire structure over both observed and latent nodes. We evaluate our method in a synthetic setting, demonstrating its ability to almost perfectly recover the ground truth clustering even at relatively low sample sizes, as well as the ability to recover a significant number of the edges from observed variables to latent factors. Finally, we apply our method in a semi-synthetic setting to protein mass spectrometry data with a known ground truth network, and achieve almost perfect recovery of the ground truth variable clusters.