Fuzzy Prediction Sets: Conformal Prediction with E-values

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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.

Comments: Shortened and more polished version

Subjects:

Statistics Theory (math.ST); Methodology (stat.ME); Machine Learning (stat.ML)

Cite as: arXiv:2509.13130 [math.ST]

(or arXiv:2509.13130v3 [math.ST] for this version)

https://doi.org/10.48550/arXiv.2509.13130

arXiv-issued DOI via DataCite

Submission history

From: Nick Koning [view email] [v1] Tue, 16 Sep 2025 14:46:18 UTC (58 KB) [v2] Fri, 14 Nov 2025 16:59:18 UTC (201 KB) [v3] Tue, 31 Mar 2026 15:07:51 UTC (205 KB)