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

arXiv · AI, language, vision and robotics · article · Sep 13, 2026 · UTC

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

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