Taming polarized fitting: BLINEX-Pcomp with asymmetric risk penalty for robust Pcomp classification

As a novel paradigm for learning with inexact supervision, Pcomp classification reduces the annotation costs of training a binary classifier by using ordered pairwise samples without requiring precise labels. However, existing methods fail to fully account for sign differences in empirical risk at the level of individual sample pairs, resulting in polarized fitting where the risks of overfitting and underfitting coexist. Actually, positive and negative empirical risks indicate varying degrees of training difficulty, necessitating differentiated treatments. In this work, we propose a BLINEX-Pcomp model that employs a bounded linear-exponential function to impose distinct penalties on positive and negative risks for each sample pair. The BLINEX-Pcomp model dynamically shifts the training focus toward challenging sample pairs, well balancing pairwise-level risks of overfitting and underfitting. Additionally, a multi-view version of BLINEX-Pcomp (MV-BLINEX-Pcomp) is developed to further enhance performance by integrating multi-view features. We have theoretically verified that MV-BLINEX-Pcomp degrades to BLINEX-Pcomp when only a single view of features is available. A dual-stage solver is designed to train the MV-BLINEX-Pcomp model. Exciting numerical results from comparative experiments validate the effectiveness of our methods in tackling Pcomp classification.