# Interventions, Where and How? Experimental Design for Causal Models at Scale

arXiv: https://arxiv.org/abs/2203.02016 · HTML: https://mlsanity.com/paper/2203.02016/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 29 of 29)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Cost-Optimal Learning of Causal Graphs](https://mlsanity.com/paper/1703.02645/) (2017)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Learning Neural Causal Models with Active Interventions](https://mlsanity.com/paper/2109.02429/) (2021)
- [Active Structure Learning of Causal DAGs via Directed Clique Tree](https://mlsanity.com/paper/2011.00641/) (2020)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Causal-BALD: Deep Bayesian Active Learning of Outcomes to Infer Treatment-Effects from Observational Data](https://mlsanity.com/paper/2111.02275/) (2021)
- [Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks](https://mlsanity.com/paper/1910.03962/) (2019)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)

## Built on by (most cited first, 30 of 49)

- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [The Essential Role of Causality in Foundation World Models for Embodied AI](https://mlsanity.com/paper/2402.06665/) (2024)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [A Meta-Reinforcement Learning Algorithm for Causal Discovery](https://mlsanity.com/paper/2207.08457/) (2022)
- [Can Large Language Models Help Experimental Design for Causal Discovery?](https://mlsanity.com/paper/2503.01139/) (2025)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [When Selection Meets Intervention: Additional Complexities in Causal Discovery](https://mlsanity.com/paper/2503.07302/) (2025)
- [On the Generalization and Adaption Performance of Causal Models](https://mlsanity.com/paper/2206.04620/) (2022)
- [A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models](https://mlsanity.com/paper/2205.10083/) (2022)
- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Advancing Deep Active Learning & Data Subset Selection: Unifying Principles with Information-Theory Intuitions](https://mlsanity.com/paper/2401.04305/) (2024)
- [Constrained Causal Bayesian Optimization](https://mlsanity.com/paper/2305.20011/) (2023)
- [CORE: Towards Scalable and Efficient Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2401.16974/) (2024)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)
- [Trust Your nabla: Gradient-based Intervention Targeting for Causal Discovery](https://mlsanity.com/paper/2211.13715/) (2022)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [CO-BED: Information-Theoretic Contextual Optimization via Bayesian Experimental Design](https://mlsanity.com/paper/2302.14015/) (2023)
- [CausalMan: A physics-based simulator for large-scale causality](https://mlsanity.com/paper/2502.12707/) (2025)
- [Near-Optimal Experiment Design in Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2509.21423/) (2025)
- [Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment Effect Estimation](https://mlsanity.com/paper/2307.04988/) (2023)
- [Simulation-based Benchmarking for Causal Structure Learning in Gene Perturbation Experiments](https://mlsanity.com/paper/2407.06015/) (2024)

## Abstract (arXiv)

Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability: factors that introduce uncertainty in estimating the underlying structural causal model (SCM). Selecting experiments (interventions) based on the uncertainty arising from both factors can expedite the identification of the SCM. Existing methods in experimental design for causal discovery from limited data either rely on linear assumptions for the SCM or select only the intervention target. This work incorporates recent advances in Bayesian causal discovery into the Bayesian optimal experimental design framework, allowing for active causal discovery of large, nonlinear SCMs while selecting both the interventional target and the value. We demonstrate the performance of the proposed method on synthetic graphs (Erdos-R`enyi, Scale Free) for both linear and nonlinear SCMs as well as on the in-silico single-cell gene regulatory network dataset, DREAM.