Scalable Gaussian Process Hyperparameter Optimization via Coverage Regularization
This work addresses the problem of efficient and accurate hyperparameter optimization for Gaussian processes, which is crucial for applications relying on uncertainty quantification, though it appears incremental by building on existing frameworks like MuyGPs.
The paper tackles the challenge of scalable hyperparameter tuning for Gaussian processes on large datasets, presenting a novel algorithm that improves uncertainty quantification robustness while maintaining scalability, as demonstrated in numerical experiments.
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.