Review of recent advances in Gaussian process regression methods

Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide inherent ways to assess the impact of uncertainties (especially in the data, and environment) on the solutions, 2) have efficient factorisation based implementations and 3) can be implemented easily in distributed manners and hence provide scalable solutions. This paper reviews the recently developed key factorised GP methods such as the hierarchical off-diagonal low-rank approximation methods and GP with Kronecker structures. An example illustrates the performance of these methods with respect to accuracy and computational complexity.