# Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs

arXiv: https://arxiv.org/abs/1303.3216 · HTML: https://mlsanity.com/paper/1303.3216/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2013.

## Built on by (most cited first, 25 of 25)

- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Abstraction between Structural Causal Models: A Review of Definitions and Properties](https://mlsanity.com/paper/2207.08603/) (2022)
- [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)
- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)
- [Valid Inference After Causal Discovery](https://mlsanity.com/paper/2208.05949/) (2022)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Variance Minimization in the Wasserstein Space for Invariant Causal Prediction](https://mlsanity.com/paper/2110.07064/) (2021)
- [On the Interventional Kullback-Leibler Divergence](https://mlsanity.com/paper/2302.05380/) (2023)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Model-based causal feature selection for general response types](https://mlsanity.com/paper/2309.12833/) (2023)
- [CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Series](https://mlsanity.com/paper/2410.02844/) (2024)
- [Causal Invariance Learning via Efficient Nonconvex Optimization](https://mlsanity.com/paper/2412.11850/) (2024)
- [Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data](https://mlsanity.com/paper/2509.25800/) (2025)
- [Federated Causal Discovery From Interventions](https://mlsanity.com/paper/2211.03846/) (2022)
- [I-FLOP: Fast Learning of Order and Parents from Interventional Data](https://mlsanity.com/paper/2608.28245/) (2026)
- [Learning Linear Gaussian Polytree Models with Interventions](https://mlsanity.com/paper/2311.04636/) (2023)
- [Efficient Identification of Direct Causal Parents via Invariance and Minimum Error Testing](https://mlsanity.com/paper/2409.12797/) (2024)
- [Causal Bayesian Optimization with Unknown Graphs](https://mlsanity.com/paper/2503.19554/) (2025)
- [Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions](https://mlsanity.com/paper/2603.02204/) (2026)
- [Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applications](https://mlsanity.com/paper/2606.06288/) (2026)
- [Relaxing Faithfulness with Intervention-Only Causal Discovery](https://mlsanity.com/paper/2607.11816/) (2026)
- [Interpretable Causal Discovery via Causal-Effect Constraints](https://mlsanity.com/paper/2608.12640/) (2026)

## Abstract (arXiv)

In many applications we have both observational and (randomized) interventional data. We propose a Gaussian likelihood framework for joint modeling of such different data-types, based on global parameters consisting of a directed acyclic graph (DAG) and correponding edge weights and error variances. Thanks to the global nature of the parameters, maximum likelihood estimation is reasonable with only one or few data points per intervention. We prove consistency of the BIC criterion for estimating the interventional Markov equivalence class of DAGs which is smaller than the observational analogue due to increased partial identifiability from interventional data. Such an improvement in identifiability has immediate implications for tighter bounds for inferring causal effects. Besides methodology and theoretical derivations, we present empirical results from real and simulated data.