2020/06/05 by Jarred Barber, Barber, Jarred · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.2006.03673
openalex publication_date 2020/06/05 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Gaussian processes are powerful models for probabilistic machine learning,\nbut are limited in application by their O(N3) inference complexity. We\npropose a method for deriving parametric families of kernel functions with\ncompact spatial support, which yield naturally sparse kernel matrices and\nenable fast Gaussian process inference via sparse linear algebra. These\nfamilies generalize known compactly-supported kernel functions, such as the\nWendland polynomials. The parameters of this family of kernels can be learned\nfrom data using maximum likelihood estimation. Alternatively, we can quickly\ncompute compact approximations of a target kernel using convex optimization. We\ndemonstrate that these approximations incur minimal error over the exact models\nwhen modeling data drawn directly from a target GP, and can out-perform the\ntraditional GP kernels on real-world signal reconstruction tasks, while\nexhibiting sub-quadratic inference complexity.\n