mlsanityData to 7 Oct 2026

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

arXiv 1303.3216 ↗First posted 13 Mar 2013math.ST stat.ME stat.THcited by 25

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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.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Mar 2013.

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Citing papers per year: 2021: 2; 2022: 6; 2023: 3; 2024: 4; 2025: 4; 2026: 6.

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  1. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  2. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  3. 2022Abstraction between Structural Causal Models: A Review of Definitions and Propertiescited by 14
  4. 2022Causal Entropy Optimizationcited by 13
  5. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12
  6. 2024Local Causal Structure Learning in the Presence of Latent Variablescited by 11
  7. 2022Valid Inference After Causal Discoverycited by 10
  8. 2025When Selection Meets Intervention: Additional Complexities in Causal Discoverycited by 9
  9. 2021Variance Minimization in the Wasserstein Space for Invariant Causal Predictioncited by 5
  10. 2023On the Interventional Kullback-Leibler Divergencecited by 5
  11. 2025Curious Causality-Seeking Agents Learn Meta Causal Worldcited by 4
  12. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
13 more
  1. 2023Model-based causal feature selection for general response typescited by 3
  2. 2024CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Seriescited by 3
  3. 2024Causal Invariance Learning via Efficient Nonconvex Optimizationcited by 2
  4. 2025Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Datacited by 2
  5. 2022Federated Causal Discovery From Interventionscited by 1
  6. 2026I-FLOP: Fast Learning of Order and Parents from Interventional Datacited by 1
  7. 2023Learning Linear Gaussian Polytree Models with Interventionscited by 0
  8. 2024Efficient Identification of Direct Causal Parents via Invariance and Minimum Error Testingcited by 0
  9. 2025Causal Bayesian Optimization with Unknown Graphscited by 0
  10. 2026Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventionscited by 0
  11. 2026Discrete Causal Representations from Heterogeneous Domains: A Bayesian Approach with Social Survey Applicationscited by 0
  12. 2026Relaxing Faithfulness with Intervention-Only Causal Discoverycited by 0
  13. 2026Interpretable Causal Discovery via Causal-Effect Constraintscited by 0