# Active Bayesian Causal Inference

arXiv: https://arxiv.org/abs/2206.02063 · HTML: https://mlsanity.com/paper/2206.02063/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 96 references that are in the map.
- First posted on arXiv 4 Jun 2022.

## Builds on (most cited first, 30 of 32)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [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)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [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)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [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)
- [Budgeted Experiment Design for Causal Structure Learning](https://mlsanity.com/paper/1709.03625/) (2017)
- [Active Invariant Causal Prediction: Experiment Selection through Stability](https://mlsanity.com/paper/2006.05690/) (2020)
- [Distinguishing cause from effect using observational data: methods and benchmarks](https://mlsanity.com/paper/1412.3773/) (2014)
- [A Bayesian Approach to Learning Causal Networks](https://mlsanity.com/paper/1302.4958/) (2013)
- [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)
- [Gaussian Process Networks](https://mlsanity.com/paper/1301.3857/) (2013)
- [Multilevel Monte Carlo estimation of expected information gains](https://mlsanity.com/paper/1811.07546/) (2018)
- [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 35)

- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (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)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (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)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Local Causal Discovery for Estimating Causal Effects](https://mlsanity.com/paper/2302.08070/) (2023)
- [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)
- [Adaptive Online Experimental Design for Causal Discovery](https://mlsanity.com/paper/2405.11548/) (2024)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Partial Structure Discovery is Sufficient for No-regret Learning in Causal Bandits](https://mlsanity.com/paper/2411.04054/) (2024)
- [CausalPlayground: Addressing Data-Generation Requirements in Cutting-Edge Causality Research](https://mlsanity.com/paper/2405.13092/) (2024)
- [Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness](https://mlsanity.com/paper/2408.03425/) (2024)
- [Sample Efficient Bayesian Learning of Causal Graphs from Interventions](https://mlsanity.com/paper/2410.20089/) (2024)
- [Generative Intervention Models for Causal Perturbation Modeling](https://mlsanity.com/paper/2411.14003/) (2024)
- [Is merging worth it? Securely evaluating the information gain for causal dataset acquisition](https://mlsanity.com/paper/2409.07215/) (2024)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Causal-EPIG: A Prediction-Oriented Active Learning Framework for CATE Estimation](https://mlsanity.com/paper/2509.21866/) (2025)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [Graph Agnostic Causal Bayesian Optimisation](https://mlsanity.com/paper/2411.03028/) (2024)
- [Causal Discovery via Bayesian Optimization](https://mlsanity.com/paper/2501.14997/) (2025)
- [ActiveCQ: Active Estimation of Causal Quantities](https://mlsanity.com/paper/2509.24293/) (2025)
- [Observationally Informed Adaptive Causal Experimental Design](https://mlsanity.com/paper/2603.03785/) (2026)
- [Online Identification of IT Systems through Active Causal Learning](https://mlsanity.com/paper/2509.02130/) (2025)
- [Large-Scale Bayesian Causal Discovery with Interventional Data](https://mlsanity.com/paper/2510.01562/) (2025)
- [Causal Preference Elicitation](https://mlsanity.com/paper/2602.01483/) (2026)

## Abstract (arXiv)

Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.