# Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions

arXiv: https://arxiv.org/abs/1802.06310 · HTML: https://mlsanity.com/paper/1802.06310/

## Key facts

- Cited by 76 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 17 Feb 2018.

## Built on by (most cited first, 30 of 76)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Linear Causal Disentanglement via Interventions](https://mlsanity.com/paper/2211.16467/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Score-based Causal Representation Learning with Interventions](https://mlsanity.com/paper/2301.08230/) (2023)
- [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)
- [Towards Robust and Adaptive Motion Forecasting: A Causal Representation Perspective](https://mlsanity.com/paper/2111.14820/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Generalizing Goal-Conditioned Reinforcement Learning with Variational Causal Reasoning](https://mlsanity.com/paper/2207.09081/) (2022)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [A Meta-Reinforcement Learning Algorithm for Causal Discovery](https://mlsanity.com/paper/2207.08457/) (2022)
- [Fine-Grained Causal Dynamics Learning with Quantization for Improving Robustness in Reinforcement Learning](https://mlsanity.com/paper/2406.03234/) (2024)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [The CausalBench challenge: A machine learning contest for gene network inference from single-cell perturbation data](https://mlsanity.com/paper/2308.15395/) (2023)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithm](https://mlsanity.com/paper/2405.18314/) (2024)
- [Competence-Based Analysis of Language Models](https://mlsanity.com/paper/2303.00333/) (2023)
- [Learning Flexible Time-windowed Granger Causality Integrating Heterogeneous Interventional Time Series Data](https://mlsanity.com/paper/2406.10419/) (2024)

## Abstract (arXiv)

We consider the problem of learning causal DAGs in the setting where both observational and interventional data is available. This setting is common in biology, where gene regulatory networks can be intervened on using chemical reagents or gene deletions. Hauser and B"uhlmann (2012) previously characterized the identifiability of causal DAGs under perfect interventions, which eliminate dependencies between targeted variables and their direct causes. In this paper, we extend these identifiability results to general interventions, which may modify the dependencies between targeted variables and their causes without eliminating them. We define and characterize the interventional Markov equivalence class that can be identified from general (not necessarily perfect) intervention experiments. We also propose the first provably consistent algorithm for learning DAGs in this setting and evaluate our algorithm on simulated and biological datasets.