Semi-Supervised Logistic Learning Based on Exponential Tilt Mixture Models

• Activity Number: 500 - Statistical Learning
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xinwei Zhang* and Zhiqiang Tan
• Companies: Rutgers University and Rutgers University
• Keywords: Semi-supervised learning; Empirical likelihood; Exponential tilt model; Fisher consistency; Logistic regression; Expectation-maximization algorithm

Abstract

Consider semi-supervised learning for classification, where both labeled and unlabeled data are available for training. The goal is to exploit both datasets to achieve higher prediction accuracy than just using labeled data alone. We develop a semi-supervised logistic learning method based on exponential tilt mixture models, by extending a statistical equivalence between logistic regression and exponential tilt modeling. We study maximum nonparametric likelihood estimation and derive novel objective functions which are shown to be Fisher probability-consistent. We also propose regularized estimation and construct simple and highly interpretable EM algorithms. Finally, we present numerical results which demonstrate the advantage of the proposed methods compared with existing methods.