Learning from Proportions of Positive and Unlabeled Examples

Weakly supervised classification tries to learn from data sets which are not certainly labeled. Many problems, with different natures of partial labeling, fit this description. In this paper, the novel problem of learning from positive‐unlabeled proportions is presented. The provided examples are unlabeled, and the only class information available consists of the proportions of positive and unlabeled examples in different subsets of the training data set. We present a methodology that adapts to the different levels of class uncertainty to learn Bayesian network classifiers using an expectation‐maximization strategy. It has been tested in a variety of artificial scenarios with different class uncertainty, as well as compared with two naive strategies that do not consider all the available class information. Finally, it has also been successfully tested in real data, collected from the embryo selection problem in assisted reproduction.

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