  Gaussian processes (GPs) are Bayesian non-parametric models useful in a
myriad of applications. Despite their popularity, the cost of GP predictions
(quadratic storage and cubic complexity with respect to the number of training
points) remains a hurdle in applying GPs to large data. We present a fast
posterior mean prediction algorithm called FastMuyGPs to address this
shortcoming. FastMuyGPs is based upon the MuyGPs hyperparameter estimation
algorithm and utilizes a combination of leave-one-out cross-validation,
batching, nearest neighbors sparsification, and precomputation to provide
scalable, fast GP prediction. We demonstrate several benchmarks wherein
FastMuyGPs prediction attains superior accuracy and competitive or superior
runtime to both deep neural networks and state-of-the-art scalable GP
algorithms.
