# A Tutorial on Learning With Bayesian Networks

arXiv: https://arxiv.org/abs/2002.00269 · HTML: https://mlsanity.com/paper/2002.00269/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 30 of 57)

- [Tractable Regularization of Probabilistic Circuits](https://mlsanity.com/paper/2106.02264/) (2021)
- [Joint Learning of Label and Environment Causal Independence for Graph Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.01103/) (2023)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)
- [Bayesian Learning for Neural Networks: an algorithmic survey](https://mlsanity.com/paper/2211.11865/) (2022)
- [MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Models](https://mlsanity.com/paper/2205.13869/) (2022)
- [Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks](https://mlsanity.com/paper/2305.16044/) (2023)
- [Nexus: An Omni-Perceptive And -Interactive Model for Language, Audio, And Vision](https://mlsanity.com/paper/2503.01879/) (2025)
- [Graph Structure and Feature Extrapolation for Out-of-Distribution Generalization](https://mlsanity.com/paper/2306.08076/) (2023)
- [Task-Driven Causal Feature Distillation: Towards Trustworthy Risk Prediction](https://mlsanity.com/paper/2312.16113/) (2023)
- [Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package](https://mlsanity.com/paper/2107.11785/) (2021)
- [Towards Digital Twin Oriented Modelling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey](https://mlsanity.com/paper/2202.09363/) (2022)
- [A Multi-Faceted Evaluation Framework for Assessing Synthetic Data Generated by Large Language Models](https://mlsanity.com/paper/2404.14445/) (2024)
- [uGLAD: Sparse graph recovery by optimizing deep unrolled networks](https://mlsanity.com/paper/2205.11610/) (2022)
- [A Sparse Quantized Hopfield Network for Online-Continual Memory](https://mlsanity.com/paper/2307.15040/) (2023)
- [The Odyssey of Commonsense Causality: From Foundational Benchmarks to Cutting-Edge Reasoning](https://mlsanity.com/paper/2406.19307/) (2024)
- [Active Structure Learning of Bayesian Networks in an Observational Setting](https://mlsanity.com/paper/2103.13796/) (2021)
- [A causal learning framework for the analysis and interpretation of COVID-19 clinical data](https://mlsanity.com/paper/2105.06998/) (2021)
- [Planning with Logical Graph-based Language Model for Instruction Generation](https://mlsanity.com/paper/2308.13782/) (2023)
- [Constructing a personalized learning path using genetic algorithms approach](https://mlsanity.com/paper/2104.11276/) (2021)
- [Coin Flipping Neural Networks](https://mlsanity.com/paper/2206.09182/) (2022)
- [On the Sparse DAG Structure Learning Based on Adaptive Lasso](https://mlsanity.com/paper/2209.02946/) (2022)
- [Near-Optimal Degree Testing for Bayes Nets](https://mlsanity.com/paper/2304.06733/) (2023)
- [Poisoning Network Flow Classifiers](https://mlsanity.com/paper/2306.01655/) (2023)
- [Prequential MDL for Causal Structure Learning with Neural Networks](https://mlsanity.com/paper/2107.05481/) (2021)
- [Feature Selection for Efficient Local-to-Global Bayesian Network Structure Learning](https://mlsanity.com/paper/2112.10369/) (2021)
- [Directed Acyclic Graphs With Tears](https://mlsanity.com/paper/2302.02160/) (2023)
- [Causal Modelling of Cryptocurrency Price Movements Using Discretisation-Aware Bayesian Networks](https://mlsanity.com/paper/2303.16148/) (2023)
- [Explaining and visualizing black-box models through counterfactual paths](https://mlsanity.com/paper/2307.07764/) (2023)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [ArrivalNet: Predicting City-wide Bus/Tram Arrival Time with Two-dimensional Temporal Variation Modeling](https://mlsanity.com/paper/2410.14742/) (2024)

## Abstract (arXiv)

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because the model encodes dependencies among all variables, it readily handles situations where some data entries are missing. Two, a Bayesian network can be used to learn causal relationships, and hence can be used to gain understanding about a problem domain and to predict the consequences of intervention. Three, because the model has both a causal and probabilistic semantics, it is an ideal representation for combining prior knowledge (which often comes in causal form) and data. Four, Bayesian statistical methods in conjunction with Bayesian networks offer an efficient and principled approach for avoiding the overfitting of data. In this paper, we discuss methods for constructing Bayesian networks from prior knowledge and summarize Bayesian statistical methods for using data to improve these models. With regard to the latter task, we describe methods for learning both the parameters and structure of a Bayesian network, including techniques for learning with incomplete data. In addition, we relate Bayesian-network methods for learning to techniques for supervised and unsupervised learning. We illustrate the graphical-modeling approach using a real-world case study.