@article{Sujon2026, 
author = {Khaled Mahmud Sujon and Adnan Shafi and Iftekhar Uddin Ahmed and Wided Bouchelligua and Amel Ksibi and Md Abdus Samad},
title = {A probabilistic fusion and meta-logistic calibration model for multiclass hybrid ensemble learning},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {17584-17634},
keywords = {hybrid ensemble learning, meta-learning, XGBoost, educational data mining, explainable AI, interpretable machine learning, statistical validation},
url = {https://www.sciopen.com/article/10.3934/math.2026719},
doi = {10.3934/math.2026719},
abstract = {Multiclass classification in educational data mining presents persistent challenges including class imbalance, miscalibrated probability outputs, and insufficient statistical validation. We proposed RXK-VEM, a hybrid ensemble framework that integrates random forest (RF), extreme gradient boosting (XGBoost), and K-nearest neighbors (KNN) through a formally defined vote-entropy-weighted meta-fusion (VEM) operator, followed by meta-level calibration using multinomial logistic regression. The VEM operator is defined as a mapping on the probability simplex        Δ          C      −      1      , aggregating heterogeneous base learner outputs into a unified probabilistic representation with provable closure properties. We further established a Rademacher complexity-based generalization bound showing that operating in the compressed    C-dimensional probability space (   C  ≪  d) tightens the generalization gap relative to classifiers trained directly on raw features, providing theoretical justification for the stacking architecture. We validated RXK-VEM on two structurally distinct educational datasets: A primary academic performance dataset (   N  =  560, five classes) from Universiti Teknologi Malaysia and a secondary student dropout dataset (   N  =  4  ,  424, three classes) from the University of California, Irvine (UCI) repository. On the primary dataset, RXK-VEM achieves 91.07% accuracy, 91.22% precision, and an 86.21% Matthews correlation coefficient (MCC), outperforming all individual base learners and conventional ensemble strategies. On the secondary dataset, the model achieves 77.30% accuracy and a 62.33% MCC, maintaining competitive performance across all metrics. Statistical validation through five-fold stratified cross-validation, paired    t-tests, and Wilcoxon signed-rank tests confirms that improvements over weaker baselines are consistent and not attributable to random variation. A systematic ablation study quantifies the complementary contribution of each base learner, and Shapley additive explanations analysis validates the interpretability of the identified predictors. The proposed framework offers a mathematically rigorous, empirically validated, and interpretable architecture for probabilistic ensemble integration in multiclass educational prediction tasks.}
}