Enhancing naive classifier for positive unlabeled data based on logistic
  regression approach
Mateusz Płatek Jan Mielniczuk
We argue that for analysis of Positive Unlabeled (PU) data under Selected
Completely At Random (SCAR) assumption it is fruitful to view the problem as
fitting of misspecified model to the data. Namely, we show that the results on
misspecified fit imply that in the case when posterior probability of the
response is modelled by logistic regression, fitting the logistic regression to
the observable PU data which {\it does not} follow this model, still yields the
vector of estimated parameters approximately colinear with the true vector of
parameters. This observation together with choosing the intercept of the
classifier based on optimisation of analogue of F1 measure yields a classifier
which performs on par or better than its competitors on several real data sets
considered.