# Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

arXiv: https://arxiv.org/abs/1302.6815 · HTML: https://mlsanity.com/paper/1302.6815/

## Key facts

- Cited by 187 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 30 of 187)

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- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
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- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Integrating Large Language Model for Improved Causal Discovery](https://mlsanity.com/paper/2306.16902/) (2023)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [Adversarial random forests for density estimation and generative modeling](https://mlsanity.com/paper/2205.09435/) (2022)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Learning Neural Causal Models with Active Interventions](https://mlsanity.com/paper/2109.02429/) (2021)
- [From Statistical to Causal Learning](https://mlsanity.com/paper/2204.00607/) (2022)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Models](https://mlsanity.com/paper/2102.10440/) (2021)
- [Differentiable Causal Discovery Under Latent Interventions](https://mlsanity.com/paper/2203.02336/) (2022)
- [CausalAF: Causal Autoregressive Flow for Safety-Critical Driving Scenario Generation](https://mlsanity.com/paper/2110.13939/) (2021)
- [Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks](https://mlsanity.com/paper/2305.16044/) (2023)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Causally Reliable Concept Bottleneck Models](https://mlsanity.com/paper/2503.04363/) (2025)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approach](https://mlsanity.com/paper/2310.06680/) (2023)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Greedy structure learning from data that contain systematic missing values](https://mlsanity.com/paper/2107.04184/) (2021)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Building Expressive and Tractable Probabilistic Generative Models: A Review](https://mlsanity.com/paper/2402.00759/) (2024)
- [Recursive Causal Discovery](https://mlsanity.com/paper/2403.09300/) (2024)

## Abstract (arXiv)

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure, statistical data, and a user's prior knowledge, and returns a score proportional to the posterior probability of the network structure given the data. The search procedure generates networks for evaluation by the scoring metric. Our contributions are threefold. First, we identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user's prior knowledge. In particular, a user can express her knowledge-for the most part-as a single prior Bayesian network for the domain. Second, we describe local search and annealing algorithms to be used in conjunction with scoring metrics. In the special case where each node has at most one parent, we show that heuristic search can be replaced with a polynomial algorithm to identify the networks with the highest score. Third, we describe a methodology for evaluating Bayesian-network learning algorithms. We apply this approach to a comparison of metrics and search procedures.