Gaussian processes are powerful tools since they can model non-linear dependencies between inputs, while remaining analytically tractable. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in their fundamental structure. It is often not clear which function structure to choose, for instance to decide between a squared exponential and a rational quadratic kernel. Based on the principle of posterior agreement, we develop a general framework for model selection to rank kernels for Gaussian process regression and compare it with maximum evidence (also called marginal likelihood) and leave-one-out cross-validation. Given the disagreement between current state-of-the-art methods in our experiments, we show the difficulty of model selection and the need for an information-theoretic approach.
CITATION STYLE
Gorbach, N. S., Bian, A. A., Fischer, B., Bauer, S., & Buhmann, J. M. (2017). Model selection for gaussian process regression. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10496 LNCS, pp. 306–318). Springer Verlag. https://doi.org/10.1007/978-3-319-66709-6_25
Mendeley helps you to discover research relevant for your work.