Uncertainty measures: The big picture
This work provides a foundational overview for researchers in AI and ML dealing with uncertainty, but it is incremental as it synthesizes existing theories without introducing new methods.
The paper organizes and critically appraises various theories of uncertainty, highlighting that probability theory is insufficient for describing second-order uncertainty and that these frameworks form clusters with different levels of generality.
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty have been proposed, many of them generalisations of classical probability. As we show here, such frameworks can be organised into clusters sharing a common rationale, exhibit complex links, and are characterised by different levels of generality. Our goal is a critical appraisal of the current landscape in uncertainty theory.