# Active Invariant Causal Prediction: Experiment Selection through Stability

arXiv: https://arxiv.org/abs/2006.05690 · HTML: https://mlsanity.com/paper/2006.05690/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2020.

## Built on by (most cited first, 30 of 37)

- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Probable Domain Generalization via Quantile Risk Minimization](https://mlsanity.com/paper/2207.09944/) (2022)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Learning Neural Causal Models with Active Interventions](https://mlsanity.com/paper/2109.02429/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Invariant Learning via Probability of Sufficient and Necessary Causes](https://mlsanity.com/paper/2309.12559/) (2023)
- [Near-Optimal Multi-Perturbation Experimental Design for Causal Structure Learning](https://mlsanity.com/paper/2105.14024/) (2021)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Causal Entropy Optimization](https://mlsanity.com/paper/2208.10981/) (2022)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Operationalizing Complex Causes: A Pragmatic View of Mediation](https://mlsanity.com/paper/2106.05074/) (2021)
- [Invariant Ancestry Search](https://mlsanity.com/paper/2202.00913/) (2022)
- [Causal Discovery using Model Invariance through Knockoff Interventions](https://mlsanity.com/paper/2207.04055/) (2022)
- [Exploiting Personalized Invariance for Better Out-of-distribution Generalization in Federated Learning](https://mlsanity.com/paper/2211.11243/) (2022)
- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)
- [Targeted Sequential Indirect Experiment Design](https://mlsanity.com/paper/2405.19985/) (2024)
- [Measure-Theoretic Anti-Causal Representation Learning](https://mlsanity.com/paper/2510.18052/) (2025)
- [Meek Separators and Their Applications in Targeted Causal Discovery](https://mlsanity.com/paper/2310.20075/) (2023)
- [Graphs Generalization under Distribution Shifts](https://mlsanity.com/paper/2403.16334/) (2024)
- [Achievable distributional robustness when the robust risk is only partially identified](https://mlsanity.com/paper/2502.02710/) (2025)
- [Automated causal inference in application to randomized controlled clinical trials](https://mlsanity.com/paper/2201.05773/) (2022)
- [Towards IID representation learning and its application on biomedical data](https://mlsanity.com/paper/2203.00332/) (2022)
- [Federated Adapter on Foundation Models: An Out-Of-Distribution Approach](https://mlsanity.com/paper/2505.01075/) (2025)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graph](https://mlsanity.com/paper/2312.05757/) (2023)
- [Revisiting Spurious Correlation in Domain Generalization](https://mlsanity.com/paper/2406.11517/) (2024)
- [Bayesian Hierarchical Invariant Prediction](https://mlsanity.com/paper/2505.11211/) (2025)

## Abstract (arXiv)

A fundamental difficulty of causal learning is that causal models can generally not be fully identified based on observational data only. Interventional data, that is, data originating from different experimental environments, improves identifiability. However, the improvement depends critically on the target and nature of the interventions carried out in each experiment. Since in real applications experiments tend to be costly, there is a need to perform the right interventions such that as few as possible are required. In this work we propose a new active learning (i.e. experiment selection) framework (A-ICP) based on Invariant Causal Prediction (ICP) (Peters et al., 2016). For general structural causal models, we characterize the effect of interventions on so-called stable sets, a notion introduced by (Pfister et al., 2019). We leverage these results to propose several intervention selection policies for A-ICP which quickly reveal the direct causes of a response variable in the causal graph while maintaining the error control inherent in ICP. Empirically, we analyze the performance of the proposed policies in both population and finite-regime experiments.