arXiv：cs.LG· Kevin Zhang, Stephen Bates·· 4 小时前AI 评分35
Conformal Prediction Sets 量化信息增益：一个理论视角
Conformal Prediction Sets Quantify Information Gain: A Theoretical Perspective
AI 导读
研究者提出基于集合值预测的决策论熵泛化框架，用 Conformal Prediction 预测集的大小与覆盖率定义一族广义信息度量，并证明 Shannon 互信息可由这些度量精确积分表示。
正文
Abstract:Conformal prediction is a popular tool for uncertainty quantification that outputs prediction sets with finite-sample coverage guarantees. While prediction set size is commonly used as a heuristic measure of uncertainty, the information-theoretic basis for this interpretation remains poorly understood. In this work, we provide such a foundation using a decision-theoretic generalization of entropy tailored to set-valued prediction. In particular, we introduce a family of generalized information measures based on the size and coverage of conformal prediction sets. Notably, Shannon mutual information admits an exact integral representation in terms of these measures. We then show that, in standard classification settings, the reduction in conformal set size from additional information (i) is sandwiched between calibration-dependent members of this family and (ii) obeys a data processing inequality, both up to finite-sample calibration and model error terms. Together, our results formally relate conformal prediction to classical information-theoretic quantities and justify using set-size reduction as an information gain metric. Empirically, we validate our theory across 11 classification settings and show that set-size reduction and Shannon mutual information can rank features differently in a greedy feature selection experiment.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.08785 [cs.LG] |
| (or arXiv:2610.08785v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.08785 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kevin Zhang [view email]
[v1]
Tue, 6 Oct 2026 17:59:11 UTC (3,712 KB)
来源：arXiv：cs.LG · arxiv.org