An efficient method for deriving confidence intervals in aggregative quantification

This paper explores efficient methods for deriving confidence intervals in quantification, the area of machine learning concerned with estimating class prevalence values. By focusing on computationally efficient strategies, we propose a robust framework for quantifying uncertainty. The key idea is to disentangle the two main phases of current aggregative quantifiers (classification followed by aggregation) and apply bootstrap only to the second phase. We investigate different methods for constructing confidence regions, including confidence intervals, confidence ellipses in the simplex, and confidence regions in the transformed Centered Log-Ratio space. Additionally, we examine various bootstrap strategies, including model-based, population-based, and a combined approach. Our results demonstrate the effectiveness of combining modelbased and population-based bootstrap approaches, particularly when used with traditional confidence intervals, while also achieving significant efficiency gains compared to a naive application of bootstrap.