Bayesian Kolmogorov-Arnold networks: Uncertainty-aware interpretable modeling through probabilistic spline decomposition

Deep learning has emerged as an essential tool in many industries, including healthcare. Traditional deep learning models lack interpretability and omit to take prediction uncertainty into account, two crucial components of clinical decision-making. In order to produce explainable and uncertainty-aware predictions, we present Bayesian Kolmogorov-Arnold Networks (Bayesian-KANs), a novel neural architecture that rigorously implements the Kolmogorov-Arnold representation theorem while providing quantified uncertainty estimates. Unlike existing KAN implementations, our method formally connects each network component to the theorem's mathematical structure through probabilistic splines. It introduces Bayesian uncertainty quantification in both inner ($\psi$) and outer ($\phi$) functions, and hence enables interpretable feature interaction analysis via uncertainty-aware decomposition. We evaluated Bayesian-KANs on four benchmark medical datasets: Pima Indians Diabetes, Cleveland Heart Disease, Breast Cancer Wisconsin (Diagnostic), and Hepatitis, and observed consistently superior performance over baseline models. Bayesian-KAN achieves accuracies of 80.1 %, 85.7 %, 96.2 %, and 88.5 %, respectively, with significantly tighter confidence intervals and higher AUC-ROC and F1 scores. Comparative analyses showed that Bayesian-KAN not only outperforms logistic regression, SVMs, traditional neural networks, and deterministic KANs in predictive accuracy, but also provides more calibrated and trustworthy uncertainty estimates. Additionally, Bayesian-KAN successfully highlights clinically relevant features in all datasets, enhancing transparency in decision-making. Moreover, Bayesian-KANs' capacity to represent aleatoric and epistemic uncertainty guarantees doctors receive more solid and trustworthy decision support. Our Bayesian strategy improves the interpretability of the model and considerably minimises overfitting, which is important for tiny and imbalanced medical datasets, according to experimental results. We present possible expansions to further use Bayesian-KANs in more complicated multimodal datasets and address the significance of these discoveries for future research in building reliable AI systems for healthcare. This work paves the way for a new paradigm in deep learning model deployment in vital sectors where transparency and reliability are crucial.