Nonstationary Covariance Functions for Gaussian Process Regression

We introduce a class of nonstationary covariance functions for Gaussian process (GP) regression. Nonstationary covariance functions allow the model to adapt to functions whose smoothness varies with the inputs. The class includes a nonstationary version of the Matérn stationary covariance, in which the differentiability of the regression function is controlled by a parameter, freeing one from fixing the differentiability in advance. In experiments, the nonstationary GP regression model performs well when the input space is two or three dimensions, outperforming a neural network model and Bayesian free-knot spline models, and competitive with a Bayesian neural network, but is outperformed in one dimension by a state-of-the-art Bayesian free-knot spline model. The model readily generalizes to non-Gaussian data. Use of computational methods for speeding GP fitting may allow for implementation of the method on larger datasets.

• Type: Conference
• Year: 2003
• Where: NIPS
• Authors: Christopher J. Paciorek, Mark J. Schervish
• Keywords: Bayesian Free-knot Spline, Free-knot Spline Model, NIPS 2003, NIPS 2007, Nonstationary Covariance Functions