BayesFL is a Java library for federated learning of Bayesian Networks (BNs), focused on three core components: Bayesian Network fusion, structure learning, and Bayesian classification. It supports multi-client environments and provides tools for discretization, evaluation, and experimental reproducibility.

Main Features

• Structural learning of BNs in federated settings.
• Federated Bayesian classifiers (generative and discriminative Naive Bayes).
• Fusion and consensus of BNs under structural or parametric constraints.
• Modular architecture for implementing and evaluating custom algorithms.
• Experimental framework for large-scale benchmarking and reproducibility.

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📁 Federated Components Overview and Project Structure

The source code is located under src/main/java/ and is divided into core and auxiliary packages.

Core Package: bayesfl/

It contains Client.java and Server.java, general components for federated execution. The Client encapsulates local learning; the Server coordinates fusion and convergence. The supported algorithms are organized into the following categories:

Structural Learning of BNs

Algorithm	Model	Fusion Type	Fusion Method(s)	Notes
BN_GES	BN	Structural	BN_FusionUnion, BN_FusionIntersection	GES variants: GES, pGES, cGES, fGES
MCT_MCTS	BN	Structural	MCT_Fusion	MCTS-based structure learning

Bayesian Classifiers

Algorithm	Model	Fusion Type	Fusion Method(s)	Notes
PT_NB	PT	Parametric	FusionPosition	WEKA Naive Bayes; parameters averaged across clients
PT_CCBN	PT	Parametric	PT_Fusion_Client, PT_Fusion_Server	Discriminative NB (wdBayes) with federated gradient updates
MiniAnDE	mAnDETree	Structural	mAnDETree_Fusion	Ensemble of reduced AnDE classifiers; fuses trees learned locally

Federated Discretization

Algorithm	Model	Fusion Type	Fusion Method	Notes
Bins_MDLP	Bins	Parametric	Bins_Fusion	Supervised discretization with global cut-point aggregation

Additional Modules

Beyond the core bayesfl package, the project includes complementary modules for structural learning and network fusion.

consensusBN/ – Structural Fusion of Bayesian Networks

• ConsensusUnion: Fusion of BNs guided by a heuristic variable ordering. Includes restricted and unrestricted alternatives.
• GeneticTreeWidthUnion: Fusion/consensus via genetic algorithms with treewidth constraints to limit the size of the resulting BNs.
• MinCutTreeWidthUnion: Consensus of BNs using min-cut analysis.

org.albacete.simd/ – Parallel and Distributed Structural Learning

• GES family: Implementations of GES, pGES, and cGES structural learning algorithm, including parallel and circular variants, and multi-threaded learning.
• MCTSBN: Monte Carlo Tree Search–based structure learning of BNs.
• MiniAnDE: MiniAnDE Bayesian classifier. A reduced version of AnDE specially designed for high-dimensional data.
• Utilities: Tools for scoring, graph handling, and experimental orchestration.

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🛠️ Installation

BayesFL uses Maven for dependency management and build automation. To compile the project and generate a runnable .jar with all dependencies:

mvn clean package

This will generate a file like:

target/bayesfl-1.0-jar-with-dependencies.jar

You can run any experiment (e.g., classification, structure learning, fusion) using:

java -jar target/bayesfl-1.0-jar-with-dependencies.jar

The default mainClass is set to bayesfl.experiments.ClusterExperiment, but you can override it if needed. For example:

java -cp target/bayesfl-1.0-jar-with-dependencies.jar bayesfl.experiments.CCBNExperiment

Dependencies

BayesFL relies principally on Tetrad for working with the structure of BNs and WEKA for classification tasks. These libraries are already included in the pom.xml file:

• Tetrad: Used for Bayesian Network structure learning and manipulation. Tetrad library
• WEKA: Used for machine learning algorithms, particularly for classification, and data management. WEKA library

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📚 Related Publications

🔄 Federated Learning (BayesFL Core)

• Pablo Torrijos, Juan C. Alfaro, José A. Gámez, José M. Puerta
  Federated Learning with Discriminative Naive Bayes Classifier
  25th International Conference on Intelligent Data Engineering and Automated Learning (IDEAL 2024)
  DOI: 10.1007/978-3-031-77738-7_27 | arXiv:2502.01532

• Pablo Torrijos, José A. Gámez, José M. Puerta
  FedGES: A Federated Learning Approach for Bayesian Network Structure Learning
  Machine Learning (2025) (Accepted for publication, extended version)*

  • Conference version: Pablo Torrijos, José A. Gámez, José M. Puerta
    FedGES: A Federated Learning Approach for Bayesian Network Structure Learning
    27th International Conference on Discovery Science (DS 2024)
    DOI: 10.1007/978-3-031-78980-9_6 | arXiv:2502.01538

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🧬 Bayesian Network Fusion (consensusBN)

• Pablo Torrijos, José M. Puerta, José A. Gámez, Juan A. Aledo
  Bayesian Network Structural Consensus via Greedy Min-Cut Analysis
  40th AAAI Conference on Artificial Intelligence (AAAI 2026) (Accepted)
  arXiv:2504.00467

• Pablo Torrijos, José A. Gámez, José M. Puerta, Juan A. Aledo
  Genetic Algorithms for Tractable Bayesian Network Fusion via Pre-Fusion Edge Pruning
  Proceedings of the Genetic and Evolutionary Computation Conference 2025 (GECCO 2025)
  DOI: 10.1145/3712256.3726333

• Pablo Torrijos, José A. Gámez, José M. Puerta
  Structural Fusion of Bayesian Networks with Limited Treewidth Using Genetic Algorithms
  IEEE Congress on Evolutionary Computation (CEC 2024)
  DOI: 10.1109/CEC60901.2024.10611976

• José M. Puerta, Juan A. Aledo, José A. Gámez, Jorge D. Laborda
  Efficient and Accurate Structural Fusion of Bayesian Networks
  Information Fusion, Vol. 66, 2021
  DOI: 10.1016/j.inffus.2020.09.003

⚙️ Parallel and Distributed BN Structural Learning (org.albacete.simd)

• Jorge D. Laborda, Pablo Torrijos, José M. Puerta, José A. Gámez
  Parallel Structural Learning of Bayesian Networks: Iterative Divide and Conquer Algorithm Based on Structural Fusion
  Knowledge-Based Systems, Vol. 296, 2024
  DOI: 10.1016/j.knosys.2024.111840

• Jorge D. Laborda, Pablo Torrijos, José M. Puerta, José A. Gámez
  Distributed Fusion-based Algorithms for Learning High-Dimensional Bayesian Networks: Testing Ring and Star Topologies
  International Journal of Approximate Reasoning, Vol. 175, 2024
  DOI: 10.1016/j.ijar.2024.109302

  • Conference version: Jorge D. Laborda, Pablo Torrijos, José M. Puerta, José A. Gámez
    A Ring-Based Distributed Algorithm for Learning High-Dimensional Bayesian Networks
    17th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2023)
    DOI: 10.1007/978-3-031-45608-4_10 | arXiv:2409.13314

🔍 MCTS BN Structural Learning (org.albacete.simd.mctsbn)

• Jorge D. Laborda, Pablo Torrijos, José M. Puerta, José A. Gámez
  Enhancing Bayesian Network Structural Learning with Monte Carlo Tree Search
  20th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2024)
  DOI: 10.1007/978-3-031-74003-9_32 | arXiv:2502.01527

📊 Bayesian Classification (org.albacete.simd.mAnDE)

• Pablo Torrijos, José A. Gámez, José M. Puerta
  MiniAnDE: A Reduced AnDE Ensemble to Deal with Microarray Data
  24th International Conference on Engineering Applications of Neural Networks (EANN / EAAAI 2023)
  DOI: 10.1007/978-3-031-34204-2_12 | arXiv:2311.12879

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📄 License

This project is licensed under the MIT License.
© 2025 Universidad de Castilla-La Mancha, Spain.