  We introduce a new observational setting for Positive Unlabeled (PU) data
where the observations at prediction time are also labeled. This occurs
commonly in practice -- we argue that the additional information is important
for prediction, and call this task "augmented PU prediction". We allow for
labeling to be feature dependent. In such scenario, Bayes classifier and its
risk is established and compared with a risk of a classifier which for
unlabeled data is based only on predictors. We introduce several variants of
the empirical Bayes rule in such scenario and investigate their performance. We
emphasise dangers (and ease) of applying classical classification rule in the
augmented PU scenario -- due to no preexisting studies, an unaware researcher
is prone to skewing the obtained predictions. We conclude that the variant
based on recently proposed variational autoencoder designed for PU scenario
works on par or better than other considered variants and yields advantage over
feature-only based methods in terms of accuracy for unlabeled samples.
