A Propagated Uncertainty Active Learning Method for Bayesian Classification Problems

Bayesian classification (BC) is a powerful supervised machine learning method for modelling the relationship between a set of continuous variables and a set of discrete variables that represent classes. BC has been successful in engineering and medical applications, including feasibility analysis and clinical diagnosis. Gaussian process (GP) models are widely used in BC methods to model the probability of assigning a class to an input point, typically through an indirect approach: a GP predicts a continuous function value based on Bayesian inference, which is then transformed into class probabilities using a nonlinear function like a sigmoid. The final class labels are assigned based on these probabilities. In this commonly used workflow, the uncertainty associated with the class prediction is usually evaluated as the uncertainty in the GP function values. A disadvantage of this approach is that it does not consider the uncertainty directly associated with the decision-making. In this work, we propagate the uncertainty from the space of GP function values to the class probability space and use this to quantify the uncertainty directly associated with the decision-making process. Additionally, we employ the propagated uncertainty as the objective function in an active learning (AL) method to generate new informative data points for the GP classifier training. We compare the proposed AL method to existing state-of-the-art methods to evaluate its performance.