From matrix inversion to constraints: provably tighter confidence regions for importance weights in label shift
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.
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BibTeX
@misc{li2026from,
title = {{From matrix inversion to constraints: provably tighter confidence regions for importance weights in label shift}},
author = {Mushan Li and Kihyun Han and Yanyuan Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14802},
eprint = {2609.14802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14802},
}
RIS
TY - UNPB
TI - From matrix inversion to constraints: provably tighter confidence regions for importance weights in label shift
AU - Mushan Li
AU - Kihyun Han
AU - Yanyuan Ma
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14802
UR - https://arxiv.org/abs/2609.14802
AB - 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.
ER -