Enhancing naive classifier for positive unlabeled data based on logistic regression approach
This addresses classification challenges in scenarios with only positive and unlabeled data, which is common in domains like medical diagnosis or fraud detection, but the approach is incremental as it builds on existing logistic regression methods.
The paper tackles the problem of classifying Positive Unlabeled (PU) data under the SCAR assumption by viewing it as fitting a misspecified logistic regression model, showing that estimated parameters are approximately colinear with true parameters, and achieves performance on par or better than competitors on several real datasets.
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.