  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.
