Robust minimax probability machines with entropy-distance Universum

Minimax probability machine is a binary classification model that minimizes the worst-case probability of misclassification. This paper introduces a robust variant of minimax probability machine integrated with Universum learning. Unlike conventional methods, the proposed approach not only operates without distributional assumptions while offering a theoretical lower bound on classification accuracy, but also leverages prior information contained in Universum samples to enhance classification performance. Additionally, a novel Universum sample selection strategy, which primarily relies on an entropy-distance criterion and additionally considers an In-Between-Universum measure, is proposed. The proposed model corresponds to an optimization problem with probability constraints, which is reformulated as a second-order cone programming problem. The model is also extended to handle nonlinearly separable datasets. Numerical experiments on both synthetic and benchmark datasets demonstrate that the proposed model achieves superior classification performance, and further validate the effectiveness of the new Universum selection strategy that incorporates the entropy-distance criterion.