2004 · 1K citations · 20 references
ComputingComputer ScienceMachine LearningOptimizationStatistical LearningGenerative ModelingOptimization For Machine LearningRepresentation LearningSemi-supervised LearningSupervised LearningEntropy MinimizationFinite Mixture ModelsModel RegularizationRegularizationSemi-supervised Models
Semi‑supervised learning seeks to learn a decision rule from both labeled and unlabeled data, and our approach subsumes other methods as special or limiting cases. We aim to motivate minimum entropy regularization as a means to incorporate unlabeled data into standard supervised learning. The method applies minimum entropy regularization and challenges mixture models when data are sampled from the distribution class spanned by the generative model. Experiments show that minimum entropy regularization improves performance, especially when generative models are misspecified or the cluster assumption is violated, and it outperforms manifold learning in high‑dimensional spaces.
We consider the semi-supervised learning problem, where a decision rule is to be learned from labeled and unlabeled data. In this framework, we motivate minimum entropy regularization, which enables to incorporate unlabeled data in the standard supervised learning. Our approach includes other approaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed solution benefits from unlabeled data. The method challenges mixture models when the data are sampled from the distribution class spanned by the generative model. The performances are definitely in favor of minimum entropy regularization when generative models are misspecified, and the weighting of unlabeled data provides robustness to the violation of the cluster assumption. Finally, we also illustrate that the method can also be far superior to manifold learning in high dimension spaces.
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Yuhai Wu, Vladimir Vapnik · Technometrics · 1999 · 27K citations
Learning with Local and Global Consistency
Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal et al. · MPG.PuRe (Max Planck Society) · 2003 · 3.8K citations · Full text