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

תקציר מקורי באנגליתarXiv:2609.14802v1 Announce Type: cross 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 regio