Marginalised Gaussian Processes with Nested SamplingDownload PDF

Published: 09 Nov 2021, Last Modified: 22 Oct 2023NeurIPS 2021 PosterReaders: Everyone
Keywords: Gaussian Processes, nested sampling, Bayesian inference
Abstract: Gaussian Process models are a rich distribution over functions with inductive biases controlled by a kernel function. Learning occurs through optimisation of the kernel hyperparameters using the marginal likelihood as the objective. This work proposes nested sampling as a means of marginalising kernel hyperparameters, because it is a technique that is well-suited to exploring complex, multi-modal distributions. We benchmark against Hamiltonian Monte Carlo on time-series and two-dimensional regression tasks, finding that a principled approach to quantifying hyperparameter uncertainty substantially improves the quality of prediction intervals.
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TL;DR: We propose nested sampling as a promising means of marginalising kernel hyperparameters.
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