# On semi-supervised estimation using exponential tilt mixture models

arXiv: https://arxiv.org/abs/2311.08504 · HTML: https://mlsanity.com/paper/2311.08504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 24 references that are in the map.
- First posted on arXiv 14 Nov 2023.

## Builds on (most cited first, 11 of 11)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Semi-Supervised Semantic Segmentation with Cross Pseudo Supervision](https://mlsanity.com/paper/2106.01226/) (2021)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Perturbed and Strict Mean Teachers for Semi-supervised Semantic Segmentation](https://mlsanity.com/paper/2111.12903/) (2021)
- [Semi-supervised Inference: General Theory and Estimation of Means](https://mlsanity.com/paper/1606.07268/) (2016)
- [Semi-supervised Inference for Explained Variance in High-dimensional Linear Regression and Its Applications](https://mlsanity.com/paper/1806.06179/) (2018)
- [Semi-Supervised Approaches to Efficient Evaluation of Model Prediction Performance](https://mlsanity.com/paper/1711.05663/) (2017)
- [High-dimensional semi-supervised learning: in search for optimal inference of the mean](https://mlsanity.com/paper/1902.00772/) (2019)
- [Semi-supervised Logistic Learning Based on Exponential Tilt Mixture Models](https://mlsanity.com/paper/1906.07882/) (2019)
- [Efficient Inference on High-Dimensional Linear Models with Missing Outcomes](https://mlsanity.com/paper/2309.06429/) (2023)

## Built on by (most cited first, 1 of 1)

- [Semi-supervised Regression Analysis with Model Misspecification and High-dimensional Data](https://mlsanity.com/paper/2406.13906/) (2024)

## Abstract (arXiv)

Consider a semi-supervised setting with a labeled dataset of binary responses and predictors and an unlabeled dataset with only the predictors. Logistic regression is equivalent to an exponential tilt model in the labeled population. For semi-supervised estimation, we develop further analysis and understanding of a statistical approach using exponential tilt mixture (ETM) models and maximum nonparametric likelihood estimation, while allowing that the class proportions may differ between the unlabeled and labeled data. We derive asymptotic properties of ETM-based estimation and demonstrate improved efficiency over supervised logistic regression in a random sampling setup and an outcome-stratified sampling setup previously used. Moreover, we reconcile such efficiency improvement with the existing semiparametric efficiency theory when the class proportions in the unlabeled and labeled data are restricted to be the same. We also provide a simulation study to numerically illustrate our theoretical findings.