Representing uncertainty and imprecision in machine learning: A survey on belief functions

Uncertainty and imprecision accompany the world we live in and occur in almost every event. How to better interpret and manage uncertainty and imprecision play a vital role in machine learning (ML). As an effective tool for modeling imperfection, the theory of belief functions (TBF) has attracted substantial attention by providing a flexible discernment of framework for effectively representing uncertainty and imprecision. To date, many TBF-based methods have been proposed in ML, but they have not yet been comprehensively summarized. This paper surveys TBF-based methods for representing uncertainty and imprecision in ML, focusing on clustering, classification and information fusion. First, we provide a formal definition of uncertainty and imprecision reasoning. On this basis, we survey the existing TBF-based methods in detail and explain how to characterize uncertainty and imprecision in the results. What is more, we discuss the current challenges in TBF-based ML and offer insightful perspectives for future research regarding clustering, classification and information fusion. This survey not only fills a critical gap in the existing literature but also serves as a guiding beacon for future explorations, emphasizing the transformative role of TBF in advancing ML methodologies.