# Learning and Testing Causal Models with Interventions

arXiv: https://arxiv.org/abs/1805.09697 · HTML: https://mlsanity.com/paper/1805.09697/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

## Built on by (most cited first, 29 of 29)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [Verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2206.15374/) (2022)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders](https://mlsanity.com/paper/2107.02772/) (2021)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledge](https://mlsanity.com/paper/2106.11560/) (2021)
- [On the Sample Complexity of Causal Discovery and the Value of Domain Expertise](https://mlsanity.com/paper/2102.03274/) (2021)
- [Learning and Testing Latent-Tree Ising Models Efficiently](https://mlsanity.com/paper/2211.13291/) (2022)
- [Collaborative Causal Discovery with Atomic Interventions](https://mlsanity.com/paper/2106.03028/) (2021)
- [On the Interventional Kullback-Leibler Divergence](https://mlsanity.com/paper/2302.05380/) (2023)
- [Learning Good Interventions in Causal Graphs via Covering](https://mlsanity.com/paper/2305.04638/) (2023)
- [Learning bounded-degree polytrees with known skeleton](https://mlsanity.com/paper/2310.06333/) (2023)
- [Causal Homotopy](https://mlsanity.com/paper/2112.01847/) (2021)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [Sample Efficient Bayesian Learning of Causal Graphs from Interventions](https://mlsanity.com/paper/2410.20089/) (2024)
- [Gaussian Mean Testing Made Simple](https://mlsanity.com/paper/2210.13706/) (2022)
- [Near-Optimal Degree Testing for Bayes Nets](https://mlsanity.com/paper/2304.06733/) (2023)
- [A continuous Structural Intervention Distance to compare Causal Graphs](https://mlsanity.com/paper/2307.16452/) (2023)
- [Causal Reasoning in Software Quality Assurance: A Systematic Review](https://mlsanity.com/paper/2408.17183/) (2024)
- [Monotonicity Testing of High-Dimensional Distributions with Subcube Conditioning](https://mlsanity.com/paper/2502.16355/) (2025)
- [Characterization and Learning of Causal Graphs from Hard Interventions](https://mlsanity.com/paper/2505.01037/) (2025)
- [Disentangling Observed Causal Effects from Latent Confounders using Method of Moments](https://mlsanity.com/paper/2101.06614/) (2021)
- [Efficient inference of interventional distributions](https://mlsanity.com/paper/2107.11712/) (2021)
- [Intervention Efficient Algorithm for Two-Stage Causal MDPs](https://mlsanity.com/paper/2111.00886/) (2021)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)
- [Asymptotic Causal Inference](https://mlsanity.com/paper/2109.09653/) (2021)
- [PAC-Causal Learnability: From Identification to Finite-Sample Guarantees](https://mlsanity.com/paper/2507.18903/) (2025)
- [Falsifying Causal Graphs With Outlier Events](https://mlsanity.com/paper/2607.12145/) (2026)

## Abstract (arXiv)

We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network M on a graph with n discrete variables and bounded in-degree and bounded `confounded components', we show that O(log n) interventions on an unknown causal Bayesian network X on the same graph, and tildeO(n/ε2) samples per intervention, suffice to efficiently distinguish whether X=M or whether there exists some intervention under which X and M are farther than ε in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: Omega(log n) interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.