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

Płatek Mateusz, Mielniczuk Jan

Annals of Computer Science and Information Systems

2023

Vol. 35

225--233

It is argued 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, it is shown 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 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.

Revisiting strategies for fitting logistic regression for positive and unlabeled data

Wawrzeńczyk Adam, Mielniczuk Jan

International Journal of Applied Mathematics and Computer Science

2022

Vol. 32, no. 2

299--309

Positive unlabeled (PU) learning is an important problem motivated by the occurrence of this type of partial observability in many applications. The present paper reconsiders recent advances in parametric modeling of PU data based on empirical likelihood maximization and argues that they can be significantly improved. The proposed approach is based on the fact that the likelihood for the logistic fit and an unknown labeling frequency can be expressed as the sum of a convex and a concave function, which is explicitly given. This allows methods such as the concave-convex procedure (CCCP) or its variant, the disciplined convex-concave procedure (DCCP), to be applied. We show by analyzing real data sets that, by using the DCCP to solve the optimization problem, we obtain significant improvements in the posterior probability and the label frequency estimation over the best available competitors.