Continuous-Space Gaussian Process Regression and Generalized Wiener Filtering with Application to Learning Curves

Gaussian process regression is a machine learning paradigm, where the regressor functions are modeled as realizations from an a priori Gaussian process model. We study abstract continuous-space Gaussian regression problems where the training set covers the whole input space instead of consisting of a finite number of distinct points. The model can be used for analyzing theoretical properties of Gaussian process regressors. In this paper, we present the general continuous-space Gaussian process regression equations and discuss their close connection with Wiener filtering. We apply the results to estimation of learning curves as functions of training set size and input dimensionality.