# Data Analysis with Bayesian Networks: A Bootstrap Approach

arXiv: https://arxiv.org/abs/1301.6695 · HTML: https://mlsanity.com/paper/1301.6695/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2013.

## Built on by (most cited first, 30 of 32)

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- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [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)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Sample, estimate, aggregate: A recipe for causal discovery foundation models](https://mlsanity.com/paper/2402.01929/) (2024)
- [Membership Inference Attacks and Generalization: A Causal Perspective](https://mlsanity.com/paper/2209.08615/) (2022)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Amortized Active Causal Induction with Deep Reinforcement Learning](https://mlsanity.com/paper/2405.16718/) (2024)
- [Bootstrap aggregation and confidence measures to improve time series causal discovery](https://mlsanity.com/paper/2306.08946/) (2023)
- [A Local Method for Identifying Causal Relations under Markov Equivalence](https://mlsanity.com/paper/2102.12685/) (2021)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)
- [Risk Assessment of Lymph Node Metastases in Endometrial Cancer Patients: A Causal Approach](https://mlsanity.com/paper/2305.10041/) (2023)
- [Goal-Oriented Sequential Bayesian Experimental Design for Causal Learning](https://mlsanity.com/paper/2507.07359/) (2025)
- [Causal Discovery on Higher-Order Interactions](https://mlsanity.com/paper/2511.14206/) (2025)
- [Causal Ensemble Agent: Hierarchical Causal Discovery with LLM-guided Expert Reweighting](https://mlsanity.com/paper/2606.10607/) (2026)
- [Joint Causal Structure and Cluster Discovery Using Variational Inference](https://mlsanity.com/paper/2608.22212/) (2026)
- [Pitfalls of Climate Network Construction: A Statistical Perspective](https://mlsanity.com/paper/2211.02888/) (2022)
- [Exploring Biomarker Relationships in Both Type 1 and Type 2 Diabetes Mellitus Through a Bayesian Network Analysis Approach](https://mlsanity.com/paper/2406.17090/) (2024)
- [BaMANI: Bayesian Multi-Algorithm causal Network Inference](https://mlsanity.com/paper/2508.11741/) (2025)
- [Stable Causal Discovery via Directed Acyclic Graph Aggregation](https://mlsanity.com/paper/2605.18633/) (2026)
- [Dynamic Structural Causal Modeling for Sleep](https://mlsanity.com/paper/2608.20285/) (2026)

## Abstract (arXiv)

In recent years there has been significant progress in algorithms and methods for inducing Bayesian networks from data. However, in complex data analysis problems, we need to go beyond being satisfied with inducing networks with high scores. We need to provide confidence measures on features of these networks: Is the existence of an edge between two nodes warranted? Is the Markov blanket of a given node robust? Can we say something about the ordering of the variables? We should be able to address these questions, even when the amount of data is not enough to induce a high scoring network. In this paper we propose Efron's Bootstrap as a computationally efficient approach for answering these questions. In addition, we propose to use these confidence measures to induce better structures from the data, and to detect the presence of latent variables.