Gaussian Process Regression for Multivariate Spectroscopic Calibration

Traditionally multivariate calibration models have been developed using regression based techniques including principal component regression and partial least squares and their non-linear counterparts. This paper proposes the application of Gaussian process regression as an alternative method for the development of a calibration model. By formulating the regression problem in a probabilistic framework, a Gaussian process is derived from the perspective of Bayesian nonparametric regression, prior to describing its implementation using Markov chain Monte Carlo methods. The flexibility of a Gaussian process, in terms of the parameterization of the covariance function, results in its good performance in terms of the development of a calibration model for both linear and non-linear data sets. To handle the high dimensionality of spectral data, principal component analysis is initially performed on the data, followed by the application of Gaussian process regression to the scores of the extracted principal components. In this sense, the proposed method is a non-linear variant of principal component regression. The effectiveness of the Gaussian process approach for the development of a calibration model is demonstrated through its application to two spectroscopic data sets. A statistical hypothesis test procedure, the paired t-test, is used to undertake an empirical comparison of the Gaussian process approach with conventional calibration techniques, and it is concluded that the Gaussian process exhibits enhanced behaviour.