A joint learning framework for Gaussian processes regression and graph learning

Abstract

In the traditional Gaussian process regression (GPR), covariance matrix of outputs is dominated by a given kernel function, that generally depends on pairwise distance or correlation between sample inputs. Nevertheless, this kind of models hardly utilize high-order statistical properties or globally topological information among sample inputs, undermining their prediction capability. To remedy this defect, we propose in this paper a novel GPR framework combining the MLE of Gaussian processes with graph learning. In our model, sample inputs are modeled by a weighted graph, whose topology is directly inferred from sample inputs based on either the smoothness assumption or the self-representative property. Such global information can be viewed as a kind of knowledge a prior, guiding the process of learning hyper-parameters of the chosen kernel function and the construction of covariance matrix of GPR model outputs. In practice, hyper-parameters of the GPR model and adjacency matrix of the graph can be trained by the alternating optimization. Theoretical analyses regarding solutions to graph learning are also presented to reduce computational complexity. Experimental results demonstrate that the proposed framework can achieve competitive performance in terms of prediction accuracies and computational efficiency, compared to state-of-the-art GPR algorithms.