Towards Handling Uncertainty-at-Source in AI -- A Review and Next Steps for Interval Regression

TL;DR

This paper reviews recent advances in interval regression for AI, emphasizing the importance of modeling uncertainty-at-source, analyzing state-of-the-art methods, and proposing extensions to ensure mathematical coherence.

Contribution

It provides a comprehensive analysis of interval-valued linear regression methods, introduces extensions for coherence, and offers practical recommendations and visualizations for better interpretability.

Findings

Interval regression methods vary in behavior and advantages.

Extensions can ensure models preserve interval properties.

Experimental results demonstrate the effectiveness of proposed methods.

Abstract

Most of statistics and AI draw insights through modelling discord or variance between sources of information (i.e., inter-source uncertainty). Increasingly, however, research is focusing upon 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 insight. Following recent progress in the capture of interval-valued data, including 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 datasets with different properties. Specific emphasis is given to the challenge of preserving mathematical coherence -- i.e., ensuring that models maintain fundamental mathematical properties of intervals throughout -- and the paper puts forward extensions to an existing approach to guarantee this. Carefully designed experiments, using both synthetic and real-world data, are conducted -- with findings presented alongside novel visualizations for interval-valued regression outputs, designed to maximise model interpretability. Finally, the paper makes recommendations concerning method suitability for data sets with specific properties and highlights remaining challenges and important next steps for developing AI with the capacity to handle uncertainty-at-source.