The use of Deep Neural Network (DNN) models in risk-based decision-making has attracted extensive attention with broad applications in medical, finance, manufacturing, and quality control. To mitigate prediction-related risks in decision making, prediction confidence or uncertainty should be assessed alongside the overall performance of algorithms. Recent studies on Bayesian deep learning helps quantify prediction uncertainty arises from input noises and model parameters. However, the normality assumption of input noise in these models limits their applicability to problems involving categorical and discrete feature variables in tabular datasets. In this paper, we propose a mathematical framework to quantify prediction uncertainty for DNN models. The prediction uncertainty arises from errors in predictors that follow some known finite discrete distribution. We then conducted a case study using the framework to predict treatment outcome for tuberculosis patients during their course of treatment. The results demonstrate under a certain level of risk, we can identify risk-sensitive cases, which are prone to be misclassified due to error in predictors. Comparing to the Monte Carlo dropout method, our proposed framework is more aware of misclassification cases. Our proposed framework for uncertainty quantification in deep learning can support risk-based decision making in applications when discrete errors in predictors are present.

翻译：深度神经网络模型在基于风险的决策中的应用引起了广泛关注，特别是在医疗、金融、制造和质量控制等领域。为降低决策中与预测相关的风险，应在评估算法整体性能的同时评估预测置信度或不确定性。近年来的贝叶斯深度学习研究有助于量化由输入噪声和模型参数引起的预测不确定性。然而，这些模型中输入噪声的正态性假设限制了其在表格数据中涉及分类和离散特征变量问题上的适用性。本文提出一个数学框架，用于量化深度神经网络模型的预测不确定性，该不确定性源于服从已知有限离散分布的预测变量误差。我们随后利用该框架开展了一项案例研究，预测结核病患者在治疗过程中的治疗结果。结果表明，在特定风险水平下，我们能够识别出因预测变量误差而易被误分类的风险敏感病例。与蒙特卡洛丢弃法相比，我们提出的框架对误分类案例具有更高的感知能力。该深度学习不确定性量化框架可在预测变量存在离散误差的应用场景中支持基于风险的决策。