# Permutation-based Causal Inference Algorithms with Interventions

arXiv: https://arxiv.org/abs/1705.10220 · HTML: https://mlsanity.com/paper/1705.10220/

## Key facts

- Cited by 78 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 30 of 78)

- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (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)
- [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)
- [Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modeling](https://mlsanity.com/paper/2211.03553/) (2022)
- [CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Data](https://mlsanity.com/paper/2210.17283/) (2022)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [Sample, estimate, aggregate: A recipe for causal discovery foundation models](https://mlsanity.com/paper/2402.01929/) (2024)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Causal Modeling with Stationary Diffusions](https://mlsanity.com/paper/2310.17405/) (2023)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Subset verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2301.03180/) (2023)
- [Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms](https://mlsanity.com/paper/2107.03863/) (2021)
- [A Meta-Reinforcement Learning Algorithm for Causal Discovery](https://mlsanity.com/paper/2207.08457/) (2022)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [Scalable Intervention Target Estimation in Linear Models](https://mlsanity.com/paper/2111.07512/) (2021)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach](https://mlsanity.com/paper/2401.10632/) (2024)
- [Variance Minimization in the Wasserstein Space for Invariant Causal Prediction](https://mlsanity.com/paper/2110.07064/) (2021)
- [A Fast Non-parametric Approach for Local Causal Structure Learning](https://mlsanity.com/paper/2111.14969/) (2021)
- [Does TabPFN Understand Causal Structures?](https://mlsanity.com/paper/2511.07236/) (2025)

## Abstract (arXiv)

Learning directed acyclic graphs using both observational and interventional data is now a fundamentally important problem due to recent technological developments in genomics that generate such single-cell gene expression data at a very large scale. In order to utilize this data for learning gene regulatory networks, efficient and reliable causal inference algorithms are needed that can make use of both observational and interventional data. In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption. These algorithms are interventional adaptations of the Greedy SP algorithm and are the first algorithms using both observational and interventional data with consistency guarantees. Moreover, these algorithms have the advantage that they are nonparametric, which makes them useful also for analyzing non-Gaussian data. In this paper, we present these two algorithms and their consistency guarantees, and we analyze their performance on simulated data, protein signaling data, and single-cell gene expression data.