Marginalised Gaussian Processes with Nested Sampling

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.

Cite

Text

Simpson et al. "Marginalised Gaussian Processes with Nested Sampling." Neural Information Processing Systems, 2021.

Markdown

[Simpson et al. "Marginalised Gaussian Processes with Nested Sampling." Neural Information Processing Systems, 2021.](https://mlanthology.org/neurips/2021/simpson2021neurips-marginalised/)

BibTeX

@inproceedings{simpson2021neurips-marginalised,
  title     = {{Marginalised Gaussian Processes with Nested Sampling}},
  author    = {Simpson, Fergus and Lalchand, Vidhi and Rasmussen, Carl Edward},
  booktitle = {Neural Information Processing Systems},
  year      = {2021},
  url       = {https://mlanthology.org/neurips/2021/simpson2021neurips-marginalised/}
}