Structured Gaussian Processes with Twin Multiple Kernel Learning

Abstract

Vanilla Gaussian processes (GPs) have prohibitive computational needs for very large data sets. To overcome this difficulty, special structures in the covariance matrix, if exist, should be exploited using decomposition methods such as the Kronecker product. In this paper, we integrated the Kronecker decomposition approach into a multiple kernel learning (MKL) framework for GP regression. We first formulated a regression algorithm with the Kronecker decomposition of structured kernels for spatiotemporal modeling to learn the contribution of spatial and temporal features as well as learning a model for out-of-sample prediction. We then evaluated the performance of our proposed computational framework, namely, structured GPs with twin MKL, on two different real data sets to show its efficiency and effectiveness. MKL helped us extract relative importance of input features by assigning weights to kernels calculated on different subsets of temporal and spatial features.