Year: 2025
Type: preprint
Abstract: Prediction sets offer a binary inclusion/exclusion for each element at the same fixed confidence level. We generalize to fuzzy prediction sets, which exclude elements at their own data-driven confidence level. Our key insight is that a fuzzy prediction set \emph{is} an e-value, capturing precisely what e-values bring to predictive inference. Fuzzy prediction sets inherit the merging properties of their e-value, offer richer guarantees to decision-makers. We also show in what sense optimal e-values give rise to optimal (fuzzy) prediction sets. We apply our results to conformal prediction, deriving optimal fuzzy conformal prediction sets, and characterizing in what sense classical conformal prediction is optimal.
Source: arXiv (Cornell University)
Authors: Koning, Nick W., van Meer, Sam
Institution: Erasmus University Rotterdam
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415317617
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