Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite

Yushi Hirose, Hiroo Irobe, Takafumi Kanamori
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2152-2178, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-hirose26a, title = {Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite}, author = {Hirose, Yushi and Irobe, Hiroo and Kanamori, Takafumi}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2152--2178}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/hirose26a/hirose26a.pdf}, url = {https://proceedings.mlr.press/v337/hirose26a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite %A Yushi Hirose %A Hiroo Irobe %A Takafumi Kanamori %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-hirose26a %I PMLR %P 2152--2178 %U https://proceedings.mlr.press/v337/hirose26a.html %V 337 %X 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.
APA
Hirose, Y., Irobe, H. & Kanamori, T.. (2026). Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2152-2178 Available from https://proceedings.mlr.press/v337/hirose26a.html.

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