Mixed Semi-Supervised Generalized-Linear-Regression with applications to Deep learning

We present a methodology for using unlabeled data to design semi supervised learning (SSL) methods that improve the prediction performance of supervised learning for regression tasks. The main idea is to design different mechanisms for integrating the unlabeled data, and include in each of them a mixing parameter $\alpha$, controlling the weight given to the unlabeled data. Focusing on Generalized-Linear-Models (GLM), we analyze the characteristics of different mixing mechanisms, and prove that in all cases, it is inevitably beneficial to integrate the unlabeled data with some non-zero mixing ratio $\alpha>0$, in terms of predictive performance. Moreover, we provide a rigorous framework for estimating the best mixing ratio $\alpha^*$ where mixed-SSL delivers the best predictive performance, while using the labeled and the unlabeled data on hand. The effectiveness of our methodology in delivering substantial improvement compared to the standard supervised models, under a variety of settings, is demonstrated empirically through extensive simulation, in a manner that supports the theoretical analysis. We also demonstrate the applicability of our methodology (with some intuitive modifications) in improving more complex models such as deep neural networks, in a real-world regression tasks.