Revisiting strategies for fitting logistic regression for positive and unlabeled data

Abstract

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.

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

“…There are some attempts to account for this, either by using Minorization-Maximization algorithm or modelling Ln (•, c) as the difference of two concave functions ( [13]). Frequently, our aim is not to approximate (β, c) but to construct a classification rule based on training data…”