Enhancing naive classifier for positive unlabeled data based on logistic regression approach

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.