指数倾斜联合偏移下的共形预测
Conformal Prediction under Exponential-Tilt Joint Shift
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中文总结 AI 辅助
针对分布偏移下共形预测覆盖率下降问题，研究指数倾斜重加权对齐（ExTRA）与预测倾斜的组合效果，发现倾斜在特定条件下可缩短集合长度，但可能损害覆盖率，何时应用仍待解决。
中文摘要 AI 辅助
当数据分布在后部署阶段发生变化时，共形预测可能会失去覆盖率。我们研究利用带标签的源数据和未标签的目标输入进行适应，允许输入分布及其与结果的关系同时发生变化。我们使用指数倾斜重加权对齐（ExTRA），该方法由Maity等人（2023）为分类问题引入，用于估计结构化分布偏移。我们比较了在共形校准中使用其估计权重与额外倾斜源预测分布两种方法。共享的学习预测器、估计权重、校准样本和测试观测值隔离了倾斜的影响。现有理论表明，两种方法在真实权重下都能达到目标覆盖率，并且在估计权重下具有共同的覆盖率界限。识别计算以及评分与权重估计误差相互作用的分析有助于解释为什么它们的性能仍然可能不同。在合成回归设置中，当假设模型与数据生成过程匹配且目标输入对偏移具有信息性时，相对于仅加权，倾斜将平均集合长度减少约30%，两种方法都达到接近标称的覆盖率。相反，在合成分类以及目标输入对响应偏移提供很少信息的回归中，倾斜可能导致显著的覆盖率损失。真实数据实验也显示没有一致的好处。仅通过加权校准获得良好的覆盖率并不能保证添加预测性倾斜会保持覆盖率。仅使用源标签和目标输入来决定何时应用这种额外调整仍然是一个开放问题。
英文摘要
Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExTRA), introduced for classification by Maity et al. (2023), to estimate structured distribution shifts. We compare using its estimated weights in conformal calibration with additionally tilting the source predictive distribution. Shared learned predictors, estimated weights, calibration samples, and test observations isolate the effect of tilting. Existing theory gives both procedures target coverage with true weights and a common coverage bound with estimated weights. Identification calculations and an analysis of how scoring interacts with weight estimation error help explain why their performance can nevertheless differ. In a synthetic regression setting where the assumed models match the data-generating process and target inputs are informative about the shift, tilting reduces mean set length by about $30\%$ relative to weighting alone, with both methods attaining coverage near nominal. Tilting can instead cause substantial coverage losses in synthetic classification and in regression when target inputs provide little information about the response shift. Real-data experiments also show no consistent benefit. Good coverage from weighted calibration alone does not ensure that adding predictive tilting will preserve coverage. Deciding when to apply this additional adjustment using only source labels and target inputs remains an open problem.
发表机构
- CROID Research（CROID研究院）
- aSSIST University（aSSIST大学）
机构由 AI 辅助整理，请以论文原文为准。
