Bayesian-Optimized Learning on Heterogeneous Multipartite Graphs: A Framework for Multi-Level Relational Data

Tuba Koç

doi:10.3390/sym17122082

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Bayesian-Optimized Learning on Heterogeneous Multipartite Graphs: A Framework for Multi-Level Relational Data

2025-12-04

Tuba Koç

Mehmet Ali Cengiz

Haydar Koç *

DOI：10.3390/sym17122082

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Abstract

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Real-world systems frequently exhibit hierarchical multipartite graph structures, yet existing graph neural network (GNN) approaches lack systematic frameworks for hyperparameter optimization in heterogeneous multi-level architectures, limiting their practical applicability. This study proposes a Bayesian optimization framework specifically designed for heterogeneous GNNs operating on three-level graph structures, addressing the computational challenges of configuring partition-aware architecture. Four GNN architectures-Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), Graph Isomorphism Networks (GINs), and GraphSAGE-were systematically evaluated using Gaussian Process-based Bayesian hyperparameter optimization with inter-partition message-passing mechanisms. The framework was validated on the TIMSS 2023 dataset (10,000 students, 789 schools, 25 countries), demonstrating that Bayesian-optimized GraphSAGE achieved the highest explained variance (R2 = 0.6187, RMSE = 71.73, MAE = 64.32) compared to seven baseline methods. Bayesian optimization substantially improved model performance, revealing that two-layer architectures optimally capture cross-partition dependencies in three-level structures. GNNExplainer was used to identify the most influential student-level features learned by the model, providing explanatory insight into how the model represents individual characteristics. The optimization framework is broadly applicable to other heterogeneous and multi-level graph settings; however, the empirical findings, such as the optimal architecture depth, are specific to hierarchical graphs with structural properties like the TIMSS topology.

Keywords:

Bayesian optimization

educational data mining

gnnexplainer

heterogeneous graph neural networks

multi-level modeling

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