Truncated covariance matrices and Toeplitz methods in gaussian processes
Amos Storkey · 1999
Gaussian processes are a limit extension of neural networks. Standard Gaussian process techniques use a squared exponential covariance function. Here, the use of truncated covariances is proposed. Such covariances have compact support. Their use speeds up matrix inversion and increases precision. Furthermore they allow the use of speedy, memory efficient Toeplitz inversion for high dimensional grid based Gaussian process predictors. 1 Introduction Gaussian process methods are a natural extension of Bayesian neural network approaches. However Gaussian processes suffer from the need to invert an n \\Theta n matrix, where n is the number of data points. This takes o(n 3 ) floating point operations. For many real life problems, there is some control over how data is collected, and this data often takes a regular form. For example data can be collected at regular time intervals or at points on a grid (e.g. video pictures) . Often this structure can be used to ensure covariance matrices ...