arXiv:2511.22823cs.LGcs.AI2025-11

统一框架解决弱监督学习不稳问题,理论保障更可靠。

A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guarantees

  • 构建统一风险最小化框架,直接建模弱监督数据结构
  • 在多种弱监督场景下均提升性能,且无需额外稳定化技巧
  • 提供理论保证,适合关注模型可靠性与泛化能力的研究者

弱监督学习在标签获取成本高或不可行时成为全监督学习的实用替代。然而,现有方法多针对特定监督模式(如正-未标记、未标记-未标记、互补标签、部分标签、相似性-未标记等),依赖后处理修正间接监督带来的不稳定性。本文提出一种原则性、统一的框架,通过直接基于弱监督数据结构构建稳定代理风险,避免后处理调整。该框架自然涵盖多种场景:正-未标记、未标记-未标记、互补标签、部分标签、多类未标记及基于元组的学习。进一步通过Rademacher复杂度建立非渐近泛化界,揭示监督结构、模型容量与样本量对性能的联合影响。分析了类别先验误设对界的影响,导出显式量化项;研究可识别性,给出充分条件(尤其通过跨组监督分层)以实现目标风险恢复。大量实验表明,该方法在不同类别先验、数据集规模和类别数下均表现一致提升,且对过拟合具有鲁棒性,无需启发式稳定策略。

原文摘要 · Abstract (English)

Weakly supervised learning has emerged as a practical alternative to fully supervised learning when complete and accurate labels are costly or infeasible to acquire. However, many existing methods are tailored to specific supervision patterns -- such as positive-unlabeled (PU), unlabeled-unlabeled (UU), complementary-label (CLL), partial-label (PLL), or similarity-unlabeled annotations -- and rely on post-hoc corrections to mitigate instability induced by indirect supervision. We propose a principled, unified framework that bypasses such post-hoc adjustments by directly formulating a stable surrogate risk grounded in the structure of weakly supervised data. The formulation naturally subsumes diverse settings -- including PU, UU, CLL, PLL, multi-class unlabeled, and tuple-based learning -- under a single optimization objective. We further establish a non-asymptotic generalization bound via Rademacher complexity that clarifies how supervision structure, model capacity, and sample size jointly govern performance. Beyond this, we analyze the effect of class-prior misspecification on the bound, deriving explicit terms that quantify its impact, and we study identifiability, giving sufficient conditions -- most notably via supervision stratification across groups -- under which the target risk is recoverable. Extensive experiments show consistent gains across class priors, dataset scales, and class counts -- without heuristic stabilization -- while exhibiting robustness to overfitting.

弱监督风险最小化理论保证统一框架

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