'Institute of Electrical and Electronics Engineers (IEEE)'
Doi
Abstract
Most of statistics and AI draw insights through modelling discord or variance between sources (i.e., inter-source) of information. Increasingly however, research is focusing on uncertainty arising at the level of individual measurements (i.e., within- or intra-source), such as for a given sensor output or human response. Here, adopting intervals rather than numbers as the fundamental data-type provides an efficient, powerful, yet challenging way forward—offering systematic capture of uncertainty-at-source, increasing informational capacity, and ultimately potential for additional insight. Following progress in the capture of interval-valued data in particular from human participants, conducting machine learning directly upon intervals is a crucial next step. This paper focuses on linear regression for interval-valued data as a recent growth area, providing an essential foundation for broader use of intervals in AI. We conduct an in-depth analysis of state-of-the-art methods, elucidating their behaviour, advantages, and pitfalls when applied to synthetic and real-world data sets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence, i.e., models maintain fundamental mathematical properties of intervals. In support of real-world applicability of the regression methods, we introduce and demonstrate a novel visualization approach, the interval regression graph, or IRG , which effectively communicates the impact of both position and range of variables within the regression models—offering a leap in their interpretability. Finally, the paper provides practical recommendations concerning regression-method choice for interval data and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source
