Learning binary classifiers only from positive and unlabeled (PU) data is an
important and challenging task in many real-world applications, including web
text classification, disease gene identification and fraud detection, where
negative samples are difficult to verify experimentally. Most recent PU
learning methods are developed based on the conventional misclassification risk
of the supervised learning type, and they require to solve the intractable risk
estimation problem by approximating the negative data distribution or the class
prior. In this paper, we introduce a variational principle for PU learning that
allows us to quantitatively evaluate the modeling error of the Bayesian
classifier directly from given data. This leads to a loss function which can be
efficiently calculated without any intermediate step or model, and a
variational learning method can then be employed to optimize the classifier
under general conditions. In addition, the discriminative performance and
numerical stability of the variational PU learning method can be further
improved by incorporating a margin maximizing loss function. We illustrate the
effectiveness of the proposed variational method on a number of benchmark
examples.

该论文介绍了一种用于正负标记样本不明确的情景下，从正样本和无标记样本中学习出二分类器的新方法 —— 使用变分原理的方法，可以直接从给定的数据中定量评估贝叶斯分类器的建模误差，并进一步提高该方法的鉴别性能和数值稳定性，还可以通过引入最大化分类间隔的损失函数来使方法更加有效。