# Characterization and Learning of Causal Graphs from Hard Interventions

arXiv: https://arxiv.org/abs/2505.01037 · HTML: https://mlsanity.com/paper/2505.01037/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 69 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 27 of 27)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Budgeted Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1709.03625/) (2017)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [Learning and Testing Causal Models with Interventions](https://mlsanity.com/paper/1805.09697/) (2018)
- [An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation](https://mlsanity.com/paper/1303.5435/) (2013)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs](https://mlsanity.com/paper/2012.09679/) (2020)
- [Revisiting the General Identifiability Problem](https://mlsanity.com/paper/2206.01081/) (2022)
- [Intervention Efficient Algorithms for Approximate Learning of Causal Graphs](https://mlsanity.com/paper/2012.13976/) (2020)
- [Sample Efficient Bayesian Learning of Causal Graphs from Interventions](https://mlsanity.com/paper/2410.20089/) (2024)
- [Lerna: Transformer Architectures for Configuring Error Correction Tools for Short- and Long-Read Genome Sequencing](https://mlsanity.com/paper/2112.10068/) (2021)
- [Bayesian causal discovery from unknown general interventions](https://mlsanity.com/paper/2312.00509/) (2023)

## Built on by (most cited first, 2 of 2)

- [Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data](https://mlsanity.com/paper/2509.25800/) (2025)
- [Relaxing Faithfulness with Intervention-Only Causal Discovery](https://mlsanity.com/paper/2607.11816/) (2026)

## Abstract (arXiv)

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.