2022/09/22 by Killian Wood, Wood, Killian, Alec M. Dunton +5 · 1 citation
Computer Science · #60G15 #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #G.3 #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2209.11280
openalex publication_date 2022/09/22 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
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.