Alec M. Dunton

Alec M. Dunton, Benjamin W. Priest, Amanda Muyskens

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.

Killian Wood, Alec M. Dunton, Amanda Muyskens et al.

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction accuracy and uncertainty; uniquely estimating multiple hyperparameters in, e.g. the Matern kernel can also be a significant challenge. Moreover, training GPs on large-scale datasets is a highly active area of research: traditional maximum likelihood hyperparameter training requires quadratic memory to form the covariance matrix and has cubic training complexity. To address the scalable hyperparameter tuning problem, we present a novel algorithm which estimates the smoothness and length-scale parameters in the Matern kernel in order to improve robustness of the resulting prediction uncertainties. Using novel loss functions similar to those in conformal prediction algorithms in the computational framework provided by the hyperparameter estimation algorithm MuyGPs, we achieve improved UQ over leave-one-out likelihood maximization while maintaining a high degree of scalability as demonstrated in numerical experiments.