Semi-supervised Gaussian process regression and its feedback design

Semi-supervised learning has received considerable attention in the machine learning literature due to its potential in reducing the need for expensive labeled data. The majority of the proposed algorithms, however, have been applied to the classification task. In this paper we present a graph-based semi-supervised algorithm for solving regression problem. Our method incorporates an adjacent graph, which is built on labeled and unlabeled data, with the standard Gaussian process (GP) prior to infer the new training and predicting distribution for semi-supervised GP regression (GPr). Additionally, in semi-supervised regression, the prediction of unlabeled data could contain some valuable information. For example, it can be seen as labeled data paired with the unlabeled data, and under some metrics, they can help to construct more accurate model. Therefore, we also describe a feedback algorithm, which can choose the useful prediction of unlabeled data for feedback to re-train the model iteratively. Experimental results show that our work achieves comparable performance to standard GPr.