  We consider a problem of learning a binary classifier only from positive data
and unlabeled data (PU learning) and estimating the class-prior in unlabeled
data under the case-control scenario. Most of the recent methods of PU learning
require an estimate of the class-prior probability in unlabeled data, and it is
estimated in advance with another method. However, such a two-step approach
which first estimates the class prior and then trains a classifier may not be
the optimal approach since the estimation error of the class-prior is not taken
into account when a classifier is trained. In this paper, we propose a novel
unified approach to estimating the class-prior and training a classifier
alternately. Our proposed method is simple to implement and computationally
efficient. Through experiments, we demonstrate the practical usefulness of the
proposed method.
