Sparse Gaussian Process Based On Hat Basis Functions

Gaussian process is a popular non-parametric Bayesian methodology for modeling the regression problem, which is completely determined by its mean and covariance function. Nevertheless, this method still has two major disadvantages: it is difficult to handle large datasets and may not meet inequality constraints in specific problems. These two issues have been addressed by the so-called sparse Gaussian process and constrained Gaussian process in recent years. In this paper, to reduce the overall computational complexity in the exact Gaussian process, we propose a new sparse Gaussian process method to solve the unconstrained regression problem. The idea is inspired by the constrained Gaussian process method. The critical point of our method is that we introduce the hat basis function, which is mentioned in the constrained Gaussian process, and modify its definition according to the range of training or test data. It turns out that this method belongs to the spectral approximation methods. Similar to the exact Gaussian process and Gaussian process with Fully Independent Training Conditional approximation, our method obtains satisfactory approximate results on analytical functions or open-source datasets.