Abstract
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.
Highlights
A wide range of commonly occurring inference problems can be fruitfully tackled using Bayesian methods
A common inference problem is that of regression; determining the relationship of a control variable x to an output variable y given a set of measurements of {yi} at points {xi}
We present two techniques that speed up the training stage of the Gaussian process regression (GPR) algorithm
Summary
A wide range of commonly occurring inference problems can be fruitfully tackled using Bayesian methods. We present modified expressions for the hyperlikelihood, its gradient and its Hessian matrix, which have all been analytically maximized and marginalized over a single-scale hyperparameter. This analytic maximization or marginalization reduces the dimensionality of the subsequent optimization problem and further speeds up the training and comparison of GPs. This analytic maximization or marginalization reduces the dimensionality of the subsequent optimization problem and further speeds up the training and comparison of GPs These techniques are useful when attempting to rapidly fit large, irregularly sampled datasets with a variety of covariance function models.
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