R: Define a Gaussian process

gp	R Documentation

Define a Gaussian process

Description

Define Gaussian processes, and project them to new coordinates.

Usage

gp(x, kernel, inducing = NULL, n = 1, tol = 1e-04)

project(f, x_new, kernel = NULL)

Arguments

`x, x_new`	greta array giving the coordinates at which to evaluate the Gaussian process
`kernel`	a kernel function created using one of the kernel() methods
`inducing`	an optional greta array giving the coordinates of inducing points in a sparse (reduced rank) Gaussian process model
`n`	the number of independent Gaussian processes to define with the same kernel
`tol`	a numerical tolerance parameter, added to the diagonal of the self-covariance matrix when computing the cholesky decomposition. If the sampler is hitting a lot of numerical errors, increasing this parameter could help
`f`	a greta array created with `gp$gp` representing the values of one or more Gaussian processes

Details

gp() returns a greta array representing the values of the Gaussian process(es) evaluated at x. This Gaussian process can be made sparse (via a reduced-rank representation of the covariance) by providing an additional set of inducing point coordinates inducing. project() evaluates the values of an existing Gaussian process (created with gp()) to new data.

Value

A greta array

Examples

## Not run: 
# build a kernel function on two dimensions
k1 <- rbf(lengthscales = c(0.1, 0.2), variance = 0.6)
k2 <- bias(variance = lognormal(0, 1))
K <- k1 + k2

# use this kernel in a full-rank Gaussian process
f <- gp(1:10, K)

# or in sparse Gaussian process
f_sparse <- gp(1:10, K, inducing = c(2, 5, 8))

# project the values of the GP to new coordinates
f_new <- project(f, 11:15)

# or project with a different kernel (e.g. a sub-kernel)
f_new_bias <- project(f, 11:15, k2)

## End(Not run)