Low‐Rank Approximation of Gaussian Process With Normal‐Gamma Prior

ABSTRACT Gaussian processes (GPs) are powerful tools to nonparameterically model stochastic functions. With regard to computation load, especially for massive data with large sample size, recent researches have applied spectral representations with stationary kernels to build low‐rank approaches to approximate GPs. However, these low‐rank methods may struggle to capture the spatially varying properties of the data in reality due to their finite representations. In this paper, we propose a novel framework for the low‐rank GPs, where a normal‐gamma prior is applied instead of the standard Gaussian prior for the coefficients in the spectral representation. The normal‐gamma prior promotes flexibility, robustness and sparsity in the low‐rank representations of GPs. An efficient hierarchical likelihood approach is also developed for estimation, which maintains the computational benefits of the low‐rank approximation. To handle the multidimensional covariates, we extend this approach to additive GPs. Numerical studies and real data examples demonstrate the performance and applicability of the proposed approaches.