From matrix inversion to constraints: provably tighter confidence regions for importance weights in label shift

2026-09-13

AI Summary

本文针对标签偏移下重要性权重估计的不确定性问题，提出一种直接矩阵约束框架，通过线性规划得到更紧致的置信区间。

Abstract

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.

Problem

• importance weights
• label shift
• finite sample uncertainty
• confidence regions
• domain adaptation

Innovation

• matrix constraint framework
• linear programming
• tighter bounds
• finite-sample validity
• confidence region geometry