Among the flourishing research of weakly supervised learning (WSL), we recognize the lack of a unified interpretation of the mechanism behind the weakly supervised scenarios, let alone a systematic treatment of the risk rewrite problem, a crucial step in the empirical risk minimization approach. In this paper, we introduce a framework providing a comprehensive understanding and a unified methodology for WSL. The formulation component of the framework, leveraging a contamination perspective, provides a unified interpretation of how weak supervision is formed and subsumes fifteen existing WSL settings. The induced reduction graphs offer comprehensive connections over WSLs. The analysis component of the framework, viewed as a decontamination process, provides a systematic method of conducting risk rewrite. In addition to the conventional inverse matrix approach, we devise a novel strategy called marginal chain aiming to decontaminate distributions. We justify the feasibility of the proposed framework by recovering existing rewrites reported in the literature.

翻译：在弱监督学习（WSL）蓬勃发展的研究中，我们注意到缺乏对弱监督场景背后机制的统一定义，更不用说对风险重写这一经验风险最小化方法关键步骤的系统化处理。本文提出一个框架，为WSL提供全面理解与统一方法论。该框架的构建部分基于污染视角，统一解释了弱监督的形成机制，并涵盖了十五种现有WSL场景。由此导出的归约图揭示了WSL之间的全面关联。框架的分析部分可视为去污染过程，提供了风险重写的系统化方法。除传统逆矩阵方法外，我们设计了一种名为边际链的新策略以实现分布去污染。通过复现文献中已有重写方法，我们验证了所提框架的可行性。