# Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets

arXiv: https://arxiv.org/abs/1403.2150 · HTML: https://mlsanity.com/paper/1403.2150/

## Key facts

- Cited by 48 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2014.

## Built on by (most cited first, 30 of 48)

- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [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 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)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [Causal Inference Through the Structural Causal Marginal Problem](https://mlsanity.com/paper/2202.01300/) (2022)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [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)
- [Obtaining Causal Information by Merging Datasets with MAXENT](https://mlsanity.com/paper/2107.07640/) (2021)
- [XInsight: eXplainable Data Analysis Through The Lens of Causality](https://mlsanity.com/paper/2207.12718/) (2022)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [A Survey of Methods, Challenges and Perspectives in Causality](https://mlsanity.com/paper/2302.00293/) (2023)
- [A Fast Non-parametric Approach for Local Causal Structure Learning](https://mlsanity.com/paper/2111.14969/) (2021)
- [Causal discovery using dynamically requested knowledge](https://mlsanity.com/paper/2310.11154/) (2023)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [Curious Causality-Seeking Agents Learn Meta Causal World](https://mlsanity.com/paper/2506.23068/) (2025)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Differentiable Invariant Causal Discovery](https://mlsanity.com/paper/2205.15638/) (2022)
- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [Formalizing Statistical Causality via Modal Logic](https://mlsanity.com/paper/2210.16751/) (2022)

## Abstract (arXiv)

Scientific practice typically involves repeatedly studying a system, each time trying to unravel a different perspective. In each study, the scientist may take measurements under different experimental conditions (interventions, manipulations, perturbations) and measure different sets of quantities (variables). The result is a collection of heterogeneous data sets coming from different data distributions. In this work, we present algorithm COmbINE, which accepts a collection of data sets over overlapping variable sets under different experimental conditions; COmbINE then outputs a summary of all causal models indicating the invariant and variant structural characteristics of all models that simultaneously fit all of the input data sets. COmbINE converts estimated dependencies and independencies in the data into path constraints on the data-generating causal model and encodes them as a SAT instance. The algorithm is sound and complete in the sample limit. To account for conflicting constraints arising from statistical errors, we introduce a general method for sorting constraints in order of confidence, computed as a function of their corresponding p-values. In our empirical evaluation, COmbINE outperforms in terms of efficiency the only pre-existing similar algorithm; the latter additionally admits feedback cycles, but does not admit conflicting constraints which hinders the applicability on real data. As a proof-of-concept, COmbINE is employed to co-analyze 4 real, mass-cytometry data sets measuring phosphorylated protein concentrations of overlapping protein sets under 3 different interventions.