arXiv：cs.LG· Siu Lun Chau, Soroush H. Zargarbashi, Yusuf Sale, Michele Caprio·· 13 小时前
超越预测集大小：用信度集几何量化共形不确定性
Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry
AI 导读
研究提出用信度集（credal set）几何来刻画共形预测的不确定性，为 split CP 建立了该表示并给出多种信度不确定性度量的解析刻画与精确算法，将原本可能指数级的计算在排序共形 p 值后降为线性时间。
正文
Abstract:Prediction-set size offers a coarse summary of conformal uncertainty. We develop a richer perspective through the geometry of credal sets: families of probability distributions compatible with conformal prediction (CP) regions. We establish this representation for split CP, extending a correspondence recently identified for full CP. Building on this representation, we derive analytical characterisations and exact algorithms for several widely used credal uncertainty measures, reducing potentially exponential computations to linear time after sorting the conformal p-values. We further unify several of these measures with classical conformal summaries by integrating set-size penalties based on Tsallis entropies across error levels. We also prove an impossibility theorem: for common split-conformal regression constructions, uncertainty summaries of the induced credal sets cannot distinguish between inputs. Classification experiments on selective prediction and distribution-shift detection show that these summaries often recover useful ranking information lost by prediction-set size at a fixed error level, enabling finer-grained uncertainty assessment. These results establish credal geometry as a principled framework for quantifying conformal uncertainty and understanding its limitations.
| Comments: | 64 pages |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2602.01667 [cs.LG] |
| (or arXiv:2602.01667v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2602.01667 arXiv-issued DOI via DataCite |
Submission history
From: Siu Lun Chau [view email]
[v1]
Mon, 2 Feb 2026 05:38:07 UTC (1,195 KB)
[v2]
Wed, 7 Oct 2026 07:35:02 UTC (513 KB)
来源：arXiv：cs.LG · arxiv.org