# Active Learning for Optimal Intervention Design in Causal Models

arXiv: https://arxiv.org/abs/2209.04744 · HTML: https://mlsanity.com/paper/2209.04744/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 109 references that are in the map.
- First posted on arXiv 10 Sep 2022.

## Builds on (most cited first, 30 of 36)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [BatchBALD: Efficient and Diverse Batch Acquisition for Deep Bayesian Active Learning](https://mlsanity.com/paper/1906.08158/) (2019)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Learning Causal Graphs with Small Interventions](https://mlsanity.com/paper/1511.00041/) (2015)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Identifying Best Interventions through Online Importance Sampling](https://mlsanity.com/paper/1701.02789/) (2017)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Causal Bandits with Unknown Graph Structure](https://mlsanity.com/paper/2106.02988/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [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)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [Bayesian Optimization for Cascade-type Multi-stage Processes](https://mlsanity.com/paper/2111.08330/) (2021)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)
- [An Experimental Design Perspective on Model-Based Reinforcement Learning](https://mlsanity.com/paper/2112.05244/) (2021)
- [A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems](https://mlsanity.com/paper/1804.07240/) (2018)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs](https://mlsanity.com/paper/2012.09679/) (2020)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models](https://mlsanity.com/paper/1803.05554/) (2018)

## Built on by (most cited first, 30 of 31)

- [Empowering Biomedical Discovery with AI Agents](https://mlsanity.com/paper/2404.02831/) (2024)
- [Active Statistical Inference](https://mlsanity.com/paper/2403.03208/) (2024)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [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)
- [Towards Causal Foundation Model: on Duality between Causal Inference and Attention](https://mlsanity.com/paper/2310.00809/) (2023)
- [Gene Regulatory Network Inference in the Presence of Dropouts: a Causal View](https://mlsanity.com/paper/2403.15500/) (2024)
- [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)
- [Prediction-Guided Active Experiments](https://mlsanity.com/paper/2411.12036/) (2024)
- [Causal Reasoning in Software Quality Assurance: A Systematic Review](https://mlsanity.com/paper/2408.17183/) (2024)
- [No Foundations without Foundations -- Why semi-mechanistic models are essential for regulatory biology](https://mlsanity.com/paper/2501.19178/) (2025)
- [Achievable distributional robustness when the robust risk is only partially identified](https://mlsanity.com/paper/2502.02710/) (2025)
- [Causal Structure and Representation Learning with Biomedical Applications](https://mlsanity.com/paper/2511.04790/) (2025)
- [Active search for Bifurcations](https://mlsanity.com/paper/2406.11141/) (2024)
- [BioBO: Biology-informed Bayesian Optimization for Perturbation Design](https://mlsanity.com/paper/2509.19988/) (2025)
- [Identifying biological perturbation targets through causal differential networks](https://mlsanity.com/paper/2410.03380/) (2024)
- [Meta-Dependence in Conditional Independence Testing](https://mlsanity.com/paper/2504.12594/) (2025)
- [Towards Identifiability of Interventional Stochastic Differential Equations](https://mlsanity.com/paper/2505.15987/) (2025)
- [Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models](https://mlsanity.com/paper/2408.10976/) (2024)
- [Learning Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2411.00213/) (2024)
- [Probabilistic Factorial Experimental Design for Combinatorial Interventions](https://mlsanity.com/paper/2506.03363/) (2025)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)
- [Simulation-free Structure Learning for Stochastic Population Dynamics](https://mlsanity.com/paper/2510.16656/) (2025)
- [LLM on a Budget: Active Knowledge Distillation for Efficient Classification of Large Text Corpora](https://mlsanity.com/paper/2511.11574/) (2025)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)
- [Many Needles in a Haystack: Active Hit Discovery for Perturbation Experiments](https://mlsanity.com/paper/2605.10196/) (2026)
- [Causal Intelligence for Constraint-Aware Intervention Design to Induce State Transitions](https://mlsanity.com/paper/2605.29008/) (2026)
- [FiGuRO: Intrinsic Dimension Estimation for Multi-Modal Data](https://mlsanity.com/paper/2608.10857/) (2026)
- [Target-Dependent Limits of Causal Repair: A Leading-Log Frontier in a Gaussian Model](https://mlsanity.com/paper/2610.00424/) (2026)

## Abstract (arXiv)

Sequential experimental design to discover interventions that achieve a desired outcome is a key problem in various domains including science, engineering and public policy. When the space of possible interventions is large, making an exhaustive search infeasible, experimental design strategies are needed. In this context, encoding the causal relationships between the variables, and thus the effect of interventions on the system, is critical for identifying desirable interventions more efficiently. Here, we develop a causal active learning strategy to identify interventions that are optimal, as measured by the discrepancy between the post-interventional mean of the distribution and a desired target mean. The approach employs a Bayesian update for the causal model and prioritizes interventions using a carefully designed, causally informed acquisition function. This acquisition function is evaluated in closed form, allowing for fast optimization. The resulting algorithms are theoretically grounded with information-theoretic bounds and provable consistency results for linear causal models with known causal graph. We apply our approach to both synthetic data and single-cell transcriptomic data from Perturb-CITE-seq experiments to identify optimal perturbations that induce a specific cell state transition. The causally informed acquisition function generally outperforms existing criteria allowing for optimal intervention design with fewer but carefully selected samples.