Semi-Supervised Empirical Risk Minimization: Using unlabeled data to improve prediction
This work addresses the challenge of leveraging unlabeled data for better predictions in machine learning, though it appears incremental as it builds on existing ERM frameworks with adaptive adjustments.
The paper tackles the problem of improving prediction performance in semi-supervised learning by developing an adaptive method based on Empirical Risk Minimization that uses unlabeled data to outperform both supervised learning and a null model, achieving substantial improvements in various settings as shown empirically.
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(1/n) 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.