  We propose a meta-learning method for positive and unlabeled (PU)
classification, which improves the performance of binary classifiers obtained
from only PU data in unseen target tasks. PU learning is an important problem
since PU data naturally arise in real-world applications such as outlier
detection and information retrieval. Existing PU learning methods require many
PU data, but sufficient data are often unavailable in practice. The proposed
method minimizes the test classification risk after the model is adapted to PU
data by using related tasks that consist of positive, negative, and unlabeled
data. We formulate the adaptation as an estimation problem of the Bayes optimal
classifier, which is an optimal classifier to minimize the classification risk.
The proposed method embeds each instance into a task-specific space using
neural networks. With the embedded PU data, the Bayes optimal classifier is
estimated through density-ratio estimation of PU densities, whose solution is
obtained as a closed-form solution. The closed-form solution enables us to
efficiently and effectively minimize the test classification risk. We
empirically show that the proposed method outperforms existing methods with one
synthetic and three real-world datasets.
