Typical semi-supervised learning (SSL) methods rely on distributional assumptions, and their performance degrades when these are violated. While PNU learning, a risk rewriting method, offers a distribution-free alternative, it is restricted to binary classification and its variance optimality remains unclear. In this paper, we propose a generalized framework that constructs unbiased risk estimators using linear combinations of component risks, subsuming PNU learning and extending to multiclass classification. We derive the minimum achievable variance, demonstrating our estimator can attain lower variance than PNU in asymmetric loss scenarios. Furthermore, we establish a generalization bound directly linking 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.
Branislav Kveton, Michal Valko, Ali Rahimi +1cs.LG
This paper proposes a novel algorithm for semisupervised learning. This algorithm learns graph cuts that maximize the margin with respect to the labels induced by the harmonic function solution. We motivate the approach, compare it to existing work, and prove a bound on its generalization error. The quality of our solutions is evaluated on a synthetic problem and three UCI ML repository datasets. In most cases, we outperform manifold regularization of support vector machines, which is a state-of-the-art approach to semi-supervised max-margin learning.