# Semi-supervised Logistic Learning Based on Exponential Tilt Mixture Models

## TL;DR

This paper introduces a semi-supervised logistic learning approach utilizing exponential tilt mixture models, enhancing classification accuracy by effectively leveraging both labeled and unlabeled data.

## Contribution

It develops a novel semi-supervised logistic method based on exponential tilt models, with new objective functions, regularized estimation, and interpretable EM algorithms.

## Key findings

- Proposed methods outperform existing semi-supervised classifiers.
- Theoretical properties such as Fisher consistency are established.
- Numerical experiments demonstrate improved prediction accuracy.

## 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 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.