# Efficient Intervention Design for Causal Discovery with Latents

arXiv: https://arxiv.org/abs/2005.11736 · HTML: https://mlsanity.com/paper/2005.11736/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2020.

## Built on by (most cited first, 22 of 22)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Generalizing Goal-Conditioned Reinforcement Learning with Variational Causal Reasoning](https://mlsanity.com/paper/2207.09081/) (2022)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [RealTCD: Temporal Causal Discovery from Interventional Data with Large Language Model](https://mlsanity.com/paper/2404.14786/) (2024)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)
- [DAG Learning on the Permutahedron](https://mlsanity.com/paper/2301.11898/) (2023)
- [Sample Constrained Treatment Effect Estimation](https://mlsanity.com/paper/2210.06594/) (2022)
- [Large-Scale Targeted Cause Discovery via Learning from Simulated Data](https://mlsanity.com/paper/2408.16218/) (2024)
- [Collaborative Causal Discovery with Atomic Interventions](https://mlsanity.com/paper/2106.03028/) (2021)
- [Evaluating Temporal Observation-Based Causal Discovery Techniques Applied to Road Driver Behaviour](https://mlsanity.com/paper/2302.00064/) (2023)
- [Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledge](https://mlsanity.com/paper/2306.11008/) (2023)
- [New metrics and search algorithms for weighted causal DAGs](https://mlsanity.com/paper/2305.04445/) (2023)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [Universal Lower Bound for Learning Causal DAGs with Atomic Interventions](https://mlsanity.com/paper/2111.05070/) (2021)
- [Experimental Design for Causal Effect Identification](https://mlsanity.com/paper/2205.02232/) (2022)
- [Identification of Average Causal Effects in Confounded Additive Noise Models](https://mlsanity.com/paper/2407.10014/) (2024)
- [Disentangling Observed Causal Effects from Latent Confounders using Method of Moments](https://mlsanity.com/paper/2101.06614/) (2021)
- [Federated Causal Discovery From Interventions](https://mlsanity.com/paper/2211.03846/) (2022)
- [Causal-aware Graph Neural Architecture Search under Distribution Shifts](https://mlsanity.com/paper/2405.16489/) (2024)
- [Design of Experiment for Discovering Directed Mixed Graph](https://mlsanity.com/paper/2509.01887/) (2025)
- [Theoretical Guarantees for Causal Discovery on Large Random Graphs](https://mlsanity.com/paper/2511.02536/) (2025)

## Abstract (arXiv)

We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process. We consider two intervention cost models: (1) a linear cost model where the cost of an intervention on a subset of variables has a linear form, and (2) an identity cost model where the cost of an intervention is the same, regardless of what variables it is on, i.e., the goal is just to minimize the number of interventions. Under the linear cost model, we give an algorithm to identify the ancestral relations of the underlying causal graph, achieving within a 2-factor of the optimal intervention cost. This approximation factor can be improved to 1+ε for any ε > 0 under some mild restrictions. Under the identity cost model, we bound the number of interventions needed to recover the entire causal graph, including the latent variables, using a parameterization of the causal graph through a special type of colliders. In particular, we introduce the notion of p-colliders, that are colliders between pair of nodes arising from a specific type of conditioning in the causal graph, and provide an upper bound on the number of interventions as a function of the maximum number of p-colliders between any two nodes in the causal graph.