Consistent One-vs-All Losses Robust to Misspecification of the Weak Label Transition Model

Learning from weak labels (including noisy, partial or complementary labels) requires exploiting the statistical dependence between ground-truth classes and observed labels. Many existing methods are built around a particular transition model, often assumed to be known, accurately estimated, or instance-independent, which leads to performance degradation under model misspecification. We introduce Convex Losses for Weak Labels (CLWL), a family of losses for weak supervision based on transforming supervised one-vs-all losses. By prioritizing classification and ranking consistency over probability calibration, CLWL relaxes rigid structural assumptions on the label transition mechanism. We provide conditions for convexity and ranking consistency, characterize the transition matrices that preserve consistency for a given loss, and show that this consistency-preserving space attains the theoretical dimension bound. We propose a constructive method for generating parametric, lower-bounded, convex losses adapted to arbitrary weak-label models. Finally, we connect CLWL to existing methods, including backward correction and some losses for partial or complementary labels. Empirical results demonstrate that CLWL outperforms state-of-the-art methods when the assumed transition model is misspecified.