Learning Safe Prediction for Semi-Supervised Regression

Semi-supervised learning (SSL) concerns how to improve performance via the usage of unlabeled data. Recent studies indicate that the usage of unlabeled data might even deteriorate performance. Although some proposals have been developed to alleviate such a fundamental challenge for semisupervised classification, the efforts on semi-supervised regression (SSR) remain to be limited. In this work we consider the learning of a safe prediction from multiple semisupervised regressors, which is not worse than a direct supervised learner with only labeled data. We cast it as a geometric projection issue with an efficient algorithm. Furthermore, we show that the proposal is provably safe and has already achieved the maximal performance gain, if the ground-truth label assignment is realized by a convex linear combination of base regressors. This provides insight to help understand safe SSR. Experimental results on a broad range of datasets validate the effectiveness of our proposal.