Computational Complexity and Training Time Synthesis of Gaussian Process Regression Kernels for Monthly Rainfall Intensity Estimation

Abstract

The precise forecasting of monthly rainfall intensity has been considered as one of the most vital topics in hydrological and climatology studies. Gaussian Process Regression (GPR) has recently emerged as a powerful non-parametric approach to machine learning capable of solving such problems. The choice of covariance function, or kernel, has some impact on the precision of the predictions and computing resources. In this paper, we will discuss how nine widely used GPR kernels, such as Matérn kernels 32 and 52, Exponential, Rational Quadratic kernels and others, affect the effectiveness and computational complexity of modeling of the approximation mapping for monthly rainfall intensity datasets. Our study has found that the optimal efficiency can be reached with the use of the following mixed kernels: ArdExponential, ArdMatérn32 and ArdMatern52 kernels. The obtained optimal efficiency can be explained by the higher suitability of such kernels regarding the intermittent behaviour of precipitation properties compared to other types of kernels. As a result, the use of the mentioned mixture kernels, namely ArdExponential, ArdMatérn32 and ArdMatern52 kernels, allows for achieving high-precision predictions while retaining efficient model architecture.