A gradient-based forward greedy algorithm for sparse Gaussian process regression

In this chaper, we present a gradient-based forward greedy method for sparse approximation of Bayesian Gaussian Process Regression (GPR) model. Different from previous work, which is mostly based on various basis vector selection strategies, we propose to construct instead of select a new basis vector at each iterative step. This idea was motivated from the well-known gradient boosting approach. The resulting algorithm built on gradient-based optimisation packages incurs similar computational cost and memory requirements to other leading sparse GPR algorithms. Moreover, the proposed work is a general framework which can be extended to deal with other popular kernel machines, including Kernel Logistic Regression (KLR) and Support Vector Machines (SVMs). Numerical experiments on a wide range of datasets are presented to demonstrate the superiority of our algorithm in terms of generalisation performance.