发表机构
School of Economics and Management, Tsinghua University（清华大学经济管理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出预测驱动的分位数学习，利用合成标签改善小样本条件下的共形预测覆盖率，在八个回归基准上验证了其有效性。
AI 中文摘要
共形预测提供了无分布假设的有限样本边际覆盖率，但事后校准数据可能过于稀少，难以学习不确定性如何随输入变化。与此同时，丰富的协变量通常可以通过领域模型或通用语言模型廉价地标注。我们研究当只有少量可信样本可用时，这些合成标签能否改善条件覆盖率。基于分数分位数回归，我们引入了预测驱动的分位数学习：一个合成标注池估计钉球风险，配对的可信与合成结果纠正其偏差，独立的可信分割执行最终共形化。对标量修正的钉球风险进行分析表明，总体条件覆盖率误差是其函数梯度；相应的海森矩阵消除全局偏移，并按边界密度对剩余形状误差加权。将此几何结构与预测驱动学习相结合，得到三资源扩展和合成效力的收益-成本规则。在八个回归基准上，合成驱动的分位数学习显著改善了下游条件覆盖率，同时保持边际有效性并产生更紧凑的预测集。一项人工评分研究发现外部大语言模型标签带来类似收益，并揭示了质量-数量-成本权衡。
英文摘要
Conformal prediction provides distribution-free finite-sample marginal coverage, but post-hoc calibration data may be too scarce to learn how uncertainty varies across inputs. Meanwhile, abundant covariates can often be labeled cheaply by domain models or general-purpose language models. We study whether these synthetic labels can improve conditional coverage when only a small trusted sample is available. Building on score-quantile regression, we introduce prediction-powered quantile learning: a synthetic-labeled pool estimates pinball risk, paired trusted and synthetic outcomes correct its bias, and an independent trusted split performs final conformalization. Profiling pinball risk over scalar corrections reveals that population conditional-coverage error is its functional gradient; the corresponding Hessian removes global shifts and weights remaining shape error by boundary density. Composing this geometry with prediction-powered learning yields a three-resource expansion and a benefit--cost rule for synthetic power. Across eight regression benchmarks, synthetic-powered quantile learning substantially improves downstream conditional coverage while preserving marginal validity and producing more compact prediction sets. A human-rating study finds similar gains from external LLM labels and exposes a quality--quantity--cost tradeoff.
