Fast methods for training Gaussian processes on large datasets.
Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise when dealing with large datasets. Here, we derive some simple results which we have found useful for speeding up the learning stage in the GPR algorithm, and especially for performing Bayesian model comparison between different covariance functions. We apply our techniques to both synthetic and real data and quantify the speed-up relative to using nested sampling to numerically evaluate model evidences.
Institute of Astronomy , Madingley Road, Cambridge CB3 0HA, UK.
C J
CJ
Moore
Institute of Astronomy , Madingley Road, Cambridge CB3 0HA, UK.
A J K
0000-0001-5242-8269
AJ
Chua
School of Physics and Astronomy, University of Birmingham , Birmingham B15 2TT, UK.
C P L
CP
Berry
School of Mathematics, University of Edinburgh and Biomathematics and Statistics Scotland , James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.
J R
JR
Gair
Gaussian processes; data analysis; inference; regression