Uncertainty Quantification in Machine Learning Predictions: A Bayesian Statistical Perspective
Keywords:
Bayesian statistics, uncertainty quantification, machine learning, probabilistic modeling, responsible AIAbstract
Machine learning (ML) has achieved remarkable success across domains such as healthcare, finance, climate science, and autonomous systems, yet the absence of reliable mechanisms to communicate predictive confidence remains a critical limitation for safe and trustworthy deployment. Uncertainty quantification (UQ) addresses this gap by enabling models to measure both aleatoric uncertainty, arising from data noise, and epistemic uncertainty, stemming from model limitations. Among various approaches, Bayesian statistics provides a principled and mathematically grounded framework for integrating prior knowledge, modeling probability distributions over parameters, and producing uncertainty-aware predictions. This paper explores the theoretical foundations of Bayesian UQ and reviews key methodologies including Monte Carlo sampling, variational inference, Gaussian processes, and Bayesian neural networks. Practical applications are examined across multiple high-stakes domains, demonstrating how Bayesian UQ enhances decision-making, fosters transparency, and aligns with ethical and regulatory standards. The study further highlights challenges such as computational cost, scalability, and prior selection, while emphasizing recent advances in approximate Bayesian methods and deep learning integration. By bridging the gap between accuracy and interpretability, Bayesian UQ strengthens trust in machine learning systems and paves the way for responsible AI adoption. Future directions are outlined, focusing on scalable frameworks, hybrid techniques, and integration with explainable AI to ensure robustness in increasingly complex environments.
References
Abdar, M., et al. (2020). A review of uncertainty quantification in deep learning: Techniques, applications and challenges. Information Fusion, 76, 243–297.
Abdar, M., Pourpanah, F., Hussain, S., Rezazadegan, D., Liu, L., Ghavamzadeh, M., … Nahavandi, S. (2020). A review of uncertainty quantification in deep learning: Application to medical image analysis. Computers in Biology and Medicine, 140, 105063.
Antorán, J., Allingham, J. U., & Hernández-Lobato, J. M. (2020). Getting a CLUE: A method for explaining uncertainty estimates. arXiv preprint arXiv:2006.06848.
Begoli, E., Bhattacharya, T., & Kusnezov, D. (2019). The need for uncertainty quantification in machine-assisted medical decision making. Nature Machine Intelligence, 1(1), 20–23.
Berger, J. O. (2013). Statistical decision theory and Bayesian analysis. Springer.
Bhatt, U., Antorán, J., Zhang, Y., Liao, Q. V., Sattigeri, P., Fogliato, R., … Weller, A. (2020). Uncertainty as a form of transparency: Measuring, communicating, and using uncertainty. Proceedings of the AAAI/ACM Conference on AI, Ethics, and Society, 401–413.
Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859–877.
Blundell, C., et al. (2015). Weight uncertainty in neural networks. Proceedings of ICML, 1613–1622.
Der Kiureghian, A., & Ditlevsen, O. (2009). Aleatory or epistemic? Does it matter? Structural Safety, 31(2), 105–112.
Gal, Y., & Ghahramani, Z. (2016). Dropout as a Bayesian approximation. Proceedings of ICML, 1050–1059.
Gelman, A., et al. (2013). Bayesian data analysis (3rd ed.). CRC Press.
Gelman, A., et al. (2017). Prior choice recommendations. Bayesian Analysis, 12(3), 515–533.
Ghahramani, Z. (2015). Probabilistic machine learning and artificial intelligence. Nature, 521(7553), 452–459.
Ghosh, S., et al. (2018). Uncertainty estimation in deep learning for disease detection. arXiv preprint arXiv:1807.01771.
Hüllermeier, E., & Waegeman, W. (2020). Aleatoric and epistemic uncertainty in machine learning. Machine Learning, 110(3), 457–506.
Jordan, M. I., & Mitchell, T. M. (2015). Machine learning: Trends, perspectives, and prospects. Science, 349(6245), 255–260.
Lakshminarayanan, B., Pritzel, A., & Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles. NeurIPS, 6402–6413.
Liu, H., Ong, Y. S., Shen, X., & Cai, J. (2020). When Gaussian process meets big data: A review of scalable GPs. IEEE Transactions on Neural Networks and Learning Systems, 31(11), 4405–4423.
Michelmore, R., et al. (2018). Evaluating uncertainty in deep learning for autonomous driving. arXiv preprint arXiv:1811.06817.
Molnar, C. (2019). Interpretable machine learning. Leanpub.
Murphy, K. P. (2012). Machine learning: A probabilistic perspective. MIT Press.
Neal, R. M. (2012). Bayesian learning for neural networks. Springer.
Ober, S. W., & Rasmussen, C. E. (2020). The promises and pitfalls of deep kernel learning. Journal of Machine Learning Research, 22(1), 1–68.
Pathiravasan, C. H., Miratrix, L. W., & Rubin, D. B. (2020). Uncertainty quantification in causal inference and predictive modeling. Annual Review of Statistics and Its Application, 8, 495–517.
Wang, H., & Yeung, D. Y. (2020). A survey on Bayesian deep learning. ACM Computing Surveys, 53(5), 1–37.
Wilson, A. G. (2020). The case for Bayesian deep learning. arXiv preprint arXiv:2001.10995
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