Learning from Partial Labels with Minimum Entropy

This paper introduces the minimum entropy regularizer for learning from partial labels. This learning problem encompasses the semi-supervised setting, where a decision rule is to be learned from labeled and unlabeled examples. The minimum entropy regularizer applies to diagnosis models, i.e. models of the posterior probabilities of classes. It is shown to include other approaches to the semi-supervised problem as particular or limiting cases. A series of experiments illustrates that the proposed criterion provides solutions taking advantage of unlabeled examples when the latter convey information. Even when the data are sampled from the distribution class spanned by a generative model, the proposed approach improves over the estimated generative model when the number of features is of the order of sample size. The performances are definitely in favor of minimum entropy when the generative model is slightly misspecified. Finally, the robustness of the learning scheme is demonstrated: in situations where unlabeled examples do not convey information, minimum entropy returns a solution discarding unlabeled examples and performs as well as supervised learning.
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