Open Access
2022 Semi-supervised empirical risk minimization: Using unlabeled data to improve prediction
Oren Yuval, Saharon Rosset
Author Affiliations +
Electron. J. Statist. 16(1): 1434-1460 (2022). DOI: 10.1214/22-EJS1985


We present a general methodology for using unlabeled data to design semi supervised learning (SSL) variants of the Empirical Risk Minimization (ERM) learning process. Focusing on generalized linear regression, we analyze of the effectiveness of our SSL approach in improving prediction performance. The key ideas are carefully considering the null model as a competitor, and utilizing the unlabeled data to determine signal-noise combinations where SSL outperforms both supervised learning and the null model. We then use SSL in an adaptive manner based on estimation of the signal and noise.

In the special case of linear regression with Gaussian covariates, we prove that the non-adaptive SSL version is in fact not capable of improving on both the supervised estimator and the null model simultaneously, beyond a negligible O(1n) term. On the other hand, the adaptive model presented in this work, can achieve a substantial improvement over both competitors simultaneously, under a variety of settings. This is shown empirically through extensive simulations, and extended to other scenarios, such as non-Gaussian covariates, misspecified linear regression, or generalized linear regression with non-linear link functions.

Funding Statement

This research was partially supported by Israeli Science Foundation grant 1804/16


Download Citation

Oren Yuval. Saharon Rosset. "Semi-supervised empirical risk minimization: Using unlabeled data to improve prediction." Electron. J. Statist. 16 (1) 1434 - 1460, 2022.


Received: 1 November 2021; Published: 2022
First available in Project Euclid: 2 March 2022

arXiv: 2009.00606
MathSciNet: MR4387847
zbMATH: 07524955
Digital Object Identifier: 10.1214/22-EJS1985

Keywords: generalized linear model , predictive modeling , semi-supervised regression

Vol.16 • No. 1 • 2022
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