Learning From M-Tuple One-vs-All Confidence Comparison Data

Partial-label learning (PLL) studies classification with ambiguous supervision, where each instance is annotated by a candidate label set that contains the unknown true label. While PLL has been widely investigated, real-world annotation pipelines often provide richer structure than an unordered set: annotators or retrieval systems may implicitly rank candidates, yielding a preferred label that is more likely to be correct, and the mis-selection patterns can be class-dependent rather than uniform. Moreover, practical candidate sets may occasionally miss the true label due to human error or imperfect upstream models. Motivated by these observations, we propose a new weak-supervision paradigm, preferred-label PLL in a one-vs-all view (PLL-OVA), where each training instance is accompanied by a candidate set and a preferred label within the set. We model preferred-label generation through a flexible noisy-channel formulation that subsumes both symmetric and asymmetric mis-selection mechanisms, and we further incorporate the missing-true-label scenario to better reflect realistic annotation noise. Building on this formulation, we develop principled empirical risk minimization (ERM) procedures via risk rewriting, establish identifiability requirements under general channels, and derive practical learning objectives that remain statistically grounded. To improve optimization stability under negative-risk effects inherent to unbiased rewriting, we introduce risk-correction functions (e.g., rectified linear unit (ReLU)/absolute value correction function (ABS)-type corrections) that significantly enhance robustness and empirical performance. Extensive experiments on benchmark datasets demonstrate that PLL-OVA consistently improves upon standard PLL baselines, especially when candidate ambiguity is large or mis-selection is nonuniform, validating the effectiveness and practicality of the proposed framework.