# Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions

arXiv: https://arxiv.org/abs/2211.14897 · HTML: https://mlsanity.com/paper/2211.14897/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 68 references that are in the map.
- First posted on arXiv 27 Nov 2022.

## Builds on (most cited first, 30 of 33)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [Invariant Causal Prediction for Sequential Data](https://mlsanity.com/paper/1706.08058/) (2017)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A Transformational Characterization of Equivalent Bayesian Network Structures](https://mlsanity.com/paper/1302.4938/) (2013)
- [Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression](https://mlsanity.com/paper/2005.14458/) (2020)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [Stabilizing Variable Selection and Regression](https://mlsanity.com/paper/1911.01850/) (2019)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Ancestral Causal Inference](https://mlsanity.com/paper/1606.07035/) (2016)
- [Cyclic Causal Discovery from Continuous Equilibrium Data](https://mlsanity.com/paper/1309.6849/) (2013)

## Built on by (most cited first, 12 of 12)

- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discovery](https://mlsanity.com/paper/2306.10816/) (2023)
- [Generative Intervention Models for Causal Perturbation Modeling](https://mlsanity.com/paper/2411.14003/) (2024)
- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Bayesian causal discovery from unknown general interventions](https://mlsanity.com/paper/2312.00509/) (2023)
- [Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guarantees](https://mlsanity.com/paper/2408.04819/) (2024)
- [Bayesian Hierarchical Invariant Prediction](https://mlsanity.com/paper/2505.11211/) (2025)
- [Less Greedy Equivalence Search](https://mlsanity.com/paper/2506.22331/) (2025)
- [Intervening to Learn and Compose Causally Disentangled Representations](https://mlsanity.com/paper/2507.04754/) (2025)
- [I-FLOP: Fast Learning of Order and Parents from Interventional Data](https://mlsanity.com/paper/2608.28245/) (2026)
- [Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling](https://mlsanity.com/paper/2503.09194/) (2025)
- [Score-Based Learning of Cluster DAGs from Interventions](https://mlsanity.com/paper/2610.11947/) (2026)

## Abstract (arXiv)

We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with additive Gaussian noise and consider interventions that perturb their targets while maintaining the causal relationships in the system. Different models may entail the same distributions, offering competing causal explanations for the given observations. We fully characterize this equivalence class and offer identifiability results, which we use to derive a greedy algorithm called GnIES to recover the equivalence class of the data-generating model without knowledge of the intervention targets. In addition, we develop a novel procedure to generate semi-synthetic data sets with known causal ground truth but distributions closely resembling those of a real data set of choice. We leverage this procedure and evaluate the performance of GnIES on an array of synthetic and semi-synthetic data sets, and real data from a biological system and a tightly controlled physical system. We provide, in the Python packages gnies and sempler, implementations of GnIES and our semi-synthetic data generation procedure.