Traditional semi-supervised learning (SSL) methods typically rely on distributional assumptions, leading to significant performance degradation when these assumptions are violated. While PNU learning, a risk rewriting method, offers a distribution-free alternative, it is limited to binary classification, and its variance optimality remains unclear. This paper proposes a generalized framework that constructs unbiased risk estimators via linear combinations of component risks, subsuming PNU learning and extending to multiclass classification.
We derive the minimum achievable variance, demonstrating that our estimator can achieve lower variance than PNU in asymmetric loss scenarios. Furthermore, we establish a generalization bound that directly links this variance reduction to improved learning performance. Based on these theoretical insights, we introduce two practical SSL methods that empirically match or outperform existing approaches on binary and multiclass benchmarks.
Blogger's Review: This paper innovatively addresses the reliance of traditional SSL methods on distributional assumptions by constructing unbiased risk estimators, providing both theoretical support and empirical results, which hold significant academic and practical value.