# Learning and scoring Gaussian latent variable causal models with unknown additive interventions

arXiv: https://arxiv.org/abs/2101.06950 · HTML: https://mlsanity.com/paper/2101.06950/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2021.

## Built on by (most cited first, 2 of 2)

- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables](https://mlsanity.com/paper/2610.06086/) (2026)

## Abstract (arXiv)

With observational data alone, causal structure learning is a challenging problem. The task becomes easier when having access to data collected from perturbations of the underlying system, even when the nature of these is unknown. Existing methods either do not allow for the presence of latent variables or assume that these remain unperturbed. However, these assumptions are hard to justify if the nature of the perturbations is unknown. We provide results that enable scoring causal structures in the setting with additive, but unknown interventions. Specifically, we propose a maximum-likelihood estimator in a structural equation model that exploits system-wide invariances to output an equivalence class of causal structures from perturbation data. Furthermore, under certain structural assumptions on the population model, we provide a simple graphical characterization of all the DAGs in the interventional equivalence class. We illustrate the utility of our framework on synthetic data as well as real data involving California reservoirs and protein expressions. The software implementation is available as the Python package utlvce.