Fast Gaussian Process Posterior Mean Prediction via Local Cross Validation and Precomputation
This addresses the scalability problem for users of Gaussian processes in large data applications, representing an incremental improvement over existing methods.
The paper tackles the computational bottleneck of Gaussian process predictions by introducing FastMuyGPs, which achieves superior accuracy and competitive or superior runtime compared to deep neural networks and state-of-the-art scalable GP algorithms in benchmarks.
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.