  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.
