A probabilistic fusion and meta-logistic calibration model for multiclass hybrid ensemble learning

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 ${\mathrm{\Delta }}^{C-1}$, 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 ( $C\ll d$) 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.