  We propose a Standing Wave Decomposition (SWD) approximation to Gaussian
Process regression (GP). GP involves a costly matrix inversion operation, which
limits applicability to large data analysis. For an input space that can be
approximated by a grid and when correlations among data are short-ranged, the
kernel matrix inversion can be replaced by analytic diagonalization using the
SWD. We show that this approach applies to uni- and multi-dimensional input
data, extends to include longer-range correlations, and the grid can be in a
latent space and used as inducing points. Through simulations, we show that our
approximate method applied to the squared exponential kernel outperforms
existing methods in predictive accuracy per unit time in the regime where data
are plentiful. Our SWD-GP is recommended for regression analyses where there is
a relatively large amount of data and/or there are constraints on computation
time.
