发表机构
CROID Research; aSSIST University（CROID研究机构; aSSIST大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对连续标签偏移下共形贝叶斯校准的脆弱性，提出联合倾斜-敏感性共形贝叶斯方法，通过敏感性分析构建有界包络，并揭示精确有效性的尾部依赖，实验验证其在弱识别偏移中的优势。
AI 中文摘要
共形贝叶斯方法将贝叶斯后验预测分数与共形校准相结合，但在连续标签偏移下，分数和校准权重均依赖于未知的响应边际密度比。现有方法通常从伪标签或预测样本中估计一个偏移参数，并将其代入校准过程。我们转而提出联合倾斜-敏感性共形贝叶斯（JTS-CB），该方法在预设的合理倾斜集合上进行敏感性分析；其分裂共形实现为JTS-SCB。每个倾斜共同决定贝叶斯共形分数和共形重要性权重。JTS-SCB在候选倾斜上形成有界敏感性包络，但其仅基于校准的构造并未继承精确的有限样本加权共形保证。因此，我们研究了一个独立的候选加权精确对应方法，并表明其有效性严重依赖于尾部行为。对于标量线性指数倾斜，任何非零候选倾斜都会使精确集合无界。更一般地，尾部增长的密度比会产生同样的病态，而具有负的\(y^2\)系数的二次倾斜具有消失的尾部权重，并允许对原始目标进行有界精确推断。当尾部增长时，比率裁剪为替代目标提供了互补的有界精确构造。实验表明，当偏移被良好识别时，强插件预测采样可以匹配预言机，而敏感性分析对于更丰富、弱识别或系统性偏差的偏移模型最为有用，但代价是预测集合更宽。
英文摘要
Conformal Bayes combines Bayesian posterior predictive scores with conformal calibration, but under continuous label shift both the score and calibration weight depend on the unknown response-marginal density ratio. Existing methods typically estimate one shift parameter from pseudo-labels or predictive samples and plug it into calibration. We instead propose Joint Tilt-Sensitivity Conformal Bayes (JTS-CB), which performs sensitivity analysis over a prespecified set of plausible tilts; its split-conformal realization is JTS-SCB. Each tilt jointly determines the Bayesian conformal score and conformal importance weight. JTS-SCB forms a bounded sensitivity envelope over candidate tilts, but its calibration-only construction does not inherit the exact finite-sample weighted-conformal guarantee. We therefore study a separate candidate-weighted exact counterpart and show that its usefulness depends sharply on tail behavior. For scalar linear exponential tilts, any nonzero candidate tilt makes the exact set unbounded. More generally, tail-growing density ratios produce the same pathology, whereas quadratic tilts with a negative coefficient on \(y^2\) have vanishing tail weights and admit bounded exact inference on the original target. Ratio clipping provides a complementary bounded exact construction for a surrogate target when tails grow. Experiments show that strong plug-in predictive sampling can match the oracle when the shift is well identified, while sensitivity analysis is most useful for richer, weakly identified, or systematically biased shift models, at the cost of wider prediction sets.
Comments47 pages
