Revisiting strategies for fitting logistic regression for positive and unlabeled data - Wawrzeńczyk, Adam; Mielniczuk, Jan (Zielona Góra: Uniwersytet Zielonogórski)
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.
Keywords: positive and unlabeled learning; empirical risk; logistic regression; concave-convex optimization