Mathematical Statistics Approaches for Explainable Artificial Intelligence Models
DOI:
https://doi.org/10.64137/3108-2637/IJMAR-V2I1P105Keywords:
Explainable Artificial Intelligence (XAI), Mathematical Statistics, Statistical Inference, Machine Learning Interpretability, Bayesian Statistics, Feature Importance, SHAP, LIME, Uncertainty Quantification, Causal Inference, Transparent AI, Trustworthy AI, Model Explainability, Statistical Learning, Fairness in AIAbstract
Explainable Artificial Intelligence (XAI) has emerged as a critical research area for improving the transparency, interpretability, fairness, and reliability of machine learning systems. As artificial intelligence models become increasingly complex, especially deep learning architectures, understanding the statistical foundations behind model behavior becomes essential for trustworthy decision-making. This paper explores the role of mathematical statistics in developing and evaluating explainable AI models. The study examines statistical inference, probability theory, hypothesis testing, Bayesian methods, regression analysis, feature importance estimation, uncertainty quantification, and causal inference as fundamental tools for interpretability. Furthermore, the paper discusses how statistical techniques contribute to local and global explanations, model validation, fairness assessment, and robustness analysis. Several widely used XAI methods, including SHAP, LIME, partial dependence plots, and counterfactual explanations, are analyzed from a statistical perspective. The paper also highlights challenges such as interpretability–accuracy trade-offs, bias propagation, high-dimensional data complexity, and uncertainty in explanations. Finally, future directions involving probabilistic explainability, statistical learning theory, and human-centered AI are presented. This work aims to bridge the gap between mathematical statistics and explainable artificial intelligence by providing a comprehensive framework for statistically grounded and trustworthy AI systems.
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