发表机构
The Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对标签偏移中重要性权重估计的不确定性，提出直接矩阵约束框架替代基于求逆的推断，通过线性规划提取边际区间，获得可证明更紧且有限样本有效的置信域，在多个基准上优于现有方法。
AI 中文摘要
重要性权重在标签偏移下的域适应中至关重要，但其效用常因估计相关的有限样本不确定性而受损。现有方法通常通过对区间值线性系统进行高斯消元来分析这种不确定性，这导致过于保守的置信域和低效的下游应用。我们提出从基于求逆的推断到直接矩阵约束框架的范式转变。我们利用该框架定义联合置信域，并通过线性规划提取边际区间，在保持精确有限样本有效性的同时，推导出重要性权重的可证明更紧的界。此外，我们分析了置信域的几何形状，并为其直径界提供了理论结果。在文本、图像、多模态基准（包括AGNews、MNIST、CIFAR-10、N24News）以及真实世界自动驾驶数据集nuImages上的评估表明，与基于求逆的方法相比，我们的方法始终产生更短的置信区间和更小的预测集。
英文摘要
Importance weights are essential in domain adaptation under label shift, yet their utility is often undermined by the finite sample uncertainty associated with their estimation. Existing methods typically analyze this uncertainty through Gaussian elimination on interval-valued linear systems, which leads to overly conservative confidence regions and inefficient downstream applications. We propose a paradigm shift from inversion-based inference to a direct matrix constraint framework. We use this framework to define a joint confidence region and extract marginal intervals via linear programming, deriving provably tighter bounds for importance weights while maintaining exact finite-sample validity. Furthermore, we analyze the confidence region's geometry and provide the theoretical results for its diameter bounds. Evaluated across text, image, multimodal benchmarks, including AGNews, MNIST, CIFAR-10, N24News, and a real-world autonomous driving dataset, nuImages, our approach consistently yields shorter confidence intervals and smaller prediction sets than inversion-based methods.
Comments36 pages, 12 figures
