Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo

Andreas Svensson, Johan Dahlin, Thomas B. Schön

Published 2015-02-06Version 1

Gaussian process regression is a popular method to model data using a non-parametric Bayesian approach. However, the hyperparameters encountered in the Gaussian process prior are often unknown, but they can still have a great influence on the posterior model. This work provides an off-the-shelf method for numerical marginalization of the hyperparameters, thus significantly alleviating the problem. Our method relies on the rigorous framework of sequential Monte Carlo, and is well suited for online problems. We demonstrate its ability to handle high-dimensional problems and compare it to other sampling methods. It is also concluded that our new method is a competitive alternative to the commonly used point estimates, empirical Bayes, both in terms of computational load and its ability to handle multimodal posteriors.