Quantifying the impact of Gaussian noise on aleatoric uncertainty in healthcare data

Abstract

Aleatoric uncertainty, arising from inherent noise in data, poses a significant challenge for deploying machine learning models in healthcare, where decisions often have high clinical stakes. Even in clean electronic health records (EHR), a baseline level of aleatoric uncertainty exists due to measurement errors, missing values, and patient variability. In this work, we investigate how Gaussian noise injection, commonly used for privacy preservation and model regularization, amplifies aleatoric uncertainty in tabular healthcare datasets. We conduct controlled experiments on two widely used datasets, Heart Disease and Diabetes, and evaluate four state-of-the-art uncertainty quantification (UQ) methods: Bayesian Neural Networks, Monte Carlo Dropout (MC-Dropout), Deep Ensembles, and Evidential Deep Learning. Our results show that aleatoric uncertainty consistently increases with noise, while classification accuracy and calibration metrics such as Negative Log Likelihood, Expected Calibration Error, and Brier Score deteriorate. Notably, Deep Ensembles demonstrate improved robustness under noise, whereas EDL captures sharper changes in uncertainty, highlighting the varied sensitivity of different UQ approaches. These findings emphasize the importance of noise-aware UQ frameworks for reliable and trustworthy deployment of machine learning systems in clinical environments.