Raghad Alamri, Michele Caprio, Gavin Brown
When a model is unsure, that uncertainty comes in two kinds: the irreducible randomness in the data (aleatoric), and the model's own ignorance from limited knowledge (epistemic). The usual approach is to invent a measure for each and defend it with axioms. This paper argues that is backwards.
Its claim is that these measures are not fundamental building blocks at all; they fall out as consequences once you commit to a loss function. Pick a strictly proper loss, decompose the resulting 'subjective risk', and the epistemic and aleatoric terms drop out on their own. With reverse cross-entropy, this recovers the familiar information-theoretic quantities, and the same recipe reproduces a grab-bag of measures other researchers had proposed separately, now under one roof. The authors then start extending the idea into learning theory.
This is drawn from the abstract, which is fairly abstract itself, so the paper is where the derivations and scope are made precise.
We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross-entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty…
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