发表机构
Department of Mathematics and Statistics, McGill University; Mila; Eli Lilly and Company（麦吉尔大学数学与统计学系; Mila; 艾莉有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何进行可靠的不确定性量化，提出等距共形预测框架，开发分割等距共形预测和转导等距共形预测两种方法，能在保持覆盖率的同时大幅降低计算成本，实现自校准和预测条件有效性。
AI 中文摘要
平均校准良好的点预测在基于自身值的条件下仍可能存在系统偏差，这削弱了其在下游决策中的应用。我们考虑可靠不确定性量化的两个目标：自校准，要求点预测在基于自身值时无偏差；预测条件有效性，要求预测区间在基于预测时达到名义覆盖率。自校准共形预测（SC-CP）在有限样本中能准确实现这两个目标，但为每个候选结果重新拟合校准器计算量过大。我们提出等距共形预测（ICP），通过拟合单个等距重新校准映射并在相似重新校准预测的分层内构建预测区间，将校准与预测集构建解耦。在此框架下我们开发了两种方法。分割等距共形预测（SICP）在有限样本中实现预测条件有效性且渐近实现自校准，代价是分割共形预测的计算量。转导等距共形预测（TICP）通过每个测试点的内循环在有限样本中准确实现两个目标，避免重新拟合等距校准器。在合成异方差回归问题和真实世界医疗利用数据集上，两种方法以低得多的计算成本达到了SC-CP的覆盖率。
英文摘要
A point prediction that is well calibrated on average can still be systematically biased conditional on its own value, undermining its use in downstream decision-making. We consider two objectives for reliable uncertainty quantification: self-calibration, requiring a point prediction to be unbiased conditional on its own value, and prediction-conditional validity, requiring a prediction interval to attain nominal coverage conditional on the prediction. Self-Calibrating Conformal Prediction (SC-CP) attains both objectives exactly in finite samples, but requires refitting its calibrator for every candidate outcome, which is computationally prohibitive for continuous outcomes. We propose Isotonic Conformal Prediction (ICP), a framework that decouples calibration from prediction-set construction by fitting a single isotonic recalibration map and constructing prediction intervals within strata of similar recalibrated predictions. Within this framework we develop two procedures. Split Isotonic Conformal Prediction (SICP) attains prediction-conditional validity in finite samples and self-calibration asymptotically, at the computational cost of split conformal prediction. Transductive Isotonic Conformal Prediction (TICP) attains both objectives exactly in finite samples through a per-test-point inner loop that avoids refitting the isotonic calibrator. On synthetic heteroscedastic regression problems and a real-world healthcare-utilization dataset, both procedures match the coverage of SC-CP at substantially lower computational cost.
