面向分布到分布回归的 Conformal Prediction 研究
Conformal Prediction for Distribution-to-Distribution Regression
AI 导读
论文研究 Conformal Prediction（CP）在分布到分布回归中的应用，指出直接套用 Split CP 得到的预测集虽边际有效但不可解释、缺乏良定义体积或可行采样过程。作者提出在正交基空间中构建预测集的新 CP 框架，在保留覆盖保证的同时产出可解释预测集，并给出温和假设下具有渐近条件覆盖的自适应变体。合成与真实数据集上的实验及公开代码验证了方法有效性。
正文 · 原文
Abstract:Conformal Prediction (CP) provides a model-agnostic framework for constructing finite-sample prediction sets with coverage guarantees and has become a tool for reliable decision-making in high-risk settings. Recent advances have extended Split Conformal Prediction to increasingly complex learning problems, including multilabel, high-dimensional, and functional outputs. In this work, we study CP for Distribution-to-Distribution Regression, a setting of growing interest across many application domains. We show that a naive application of Split CP yields prediction sets that, while marginally valid, are non-interpretable, e.g., lacking a well-defined volume or a tractable sampling procedure, and of limited practical value. To overcome this, we propose a new conformal framework that operates in an orthogonal basis space, producing interpretable prediction sets while preserving coverage guarantees. We further develop an adaptive variant with asymptotic conditional coverage under mild assumptions. Empirical results on synthetic and real-world datasets validate the effectiveness of the proposed approach. The code is publicly available at this https URL.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.06320 [cs.LG] |
| (or arXiv:2611.06320v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.06320 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Khang Tran [view email]
[v1]
Wed, 4 Nov 2026 10:54:16 UTC (1,081 KB)
来源：arXiv cs.AI · arxiv.org