解决实际部署中数据分布偏移下的置信预测难题，给出可计算的风险后验。
Weighted Bayesian Conformal Prediction
- 基于狄利克雷过程与似然比权重，构建部署风险的精确贝叶斯后验。
- 在真实分布偏移下，实际失败率接近目标值，而传统方法严重偏离。
- 输出每个阈值的风险后验，而非单一数值，适合高可靠性场景。
机器学习模型很少部署在与训练数据相同的分布上。分位数预测及其风险控制扩展能在部署时提供无分布假设的保证，但仅在可交换性或已知似然比的协变量偏移下成立——而实践中更常见的是似然比需估计的情况，这正是现有贝叶斯方法无法处理的开放问题。本文从新视角出发：将狄利克雷过程先验作用于校准分布，通过似然比权重得到部署风险的精确贝叶斯后验。该后验依赖于部署时估计的权重函数，因此进一步证明了风险阈值实际承担风险的有限样本上下界，以权重估计误差和条件偏移为参数。在合成与真实协变量偏移场景下，回归与分类任务中，所提方法的实际失败率始终贴近目标水平，而传统盲选方法则显著偏离。部署结果为每个阈值提供风险后验，而非单一数值。
原文摘要 · Abstract (English)
Machine learning predictors are rarely deployed on data that match the data they were calibrated on. Conformal prediction and its risk-control generalization promise distribution-free guarantees at deployment, but only under exchangeability or a covariate shift whose likelihood ratio is known exactly -- and the estimated-ratio case, the one that occurs in practice, is explicitly open, out of reach of the Bayesian construction available under exchangeability. We reach it from a different starting point: pushing a Dirichlet process prior on the calibration distribution through the likelihood ratio yields the exact Bayesian posterior over the deployed risk. That posterior is exact given the weight function, which at deployment is itself estimated, so we further prove finite-sample upper and lower bounds on the risk the selected threshold actually incurs, in terms of the weight-estimation error and the conditional shift. On synthetic and real covariate shifts, in regression and classification, the realized failure rate then stays close to target where shift-blind selection fails, and what deployment receives is a posterior over the risk of every threshold rather than a single number.
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