Selection of covariance functions in Gaussian process-based soft sensors

Gaussian processes are emerging as a new option in soft sensor building techniques. They can provide predictions with associated uncertainty measure that can be of great importance in open and closed loop control applications. Most importantly, they have a relatively simple model structure as they are totally determined by their mean and covariance functions. The selection of the covariance function determines the overall performance of the soft sensor. This paper conducts an empirical comparison using 8 different data sets from various industrial applications between the squared exponential covariance function - used in all previously published Gaussian process-based soft sensors - and the Matérn class covariance function. The contribution of the paper is to recommend the use of the Matérn class covariance function for soft sensors, since in our experiments its accuracy is at least that of the squared exponential covariance function, and in some cases higher. In addition, results on condition numbers indicate that the Matérn class covariance function results in a prediction model that is less sensitive to numerical errors.