The Pessimistic Limits and Possibilities of Margin-based Losses in Semi-supervised Learning
This addresses theoretical limitations in semi-supervised learning for classification, providing insights into when improvements are feasible, though it is incremental as it builds on existing loss function analysis.
The paper shows that for linear classifiers using decreasing convex margin-based losses, no semi-supervised method can guarantee improvement over supervised learning, but for increasing convex losses, safe improvements are possible.
Consider a classification problem where we have both labeled and unlabeled data available. We show that for linear classifiers defined by convex margin-based surrogate losses that are decreasing, it is impossible to construct any semi-supervised approach that is able to guarantee an improvement over the supervised classifier measured by this surrogate loss on the labeled and unlabeled data. For convex margin-based loss functions that also increase, we demonstrate safe improvements are possible.