Perform Gaussian processes prediction (under isotropic or separable formulation)
at new XX locations using a GP object stored on the C-side
predGP(gpi, XX, lite = FALSE, nonug = FALSE)
predGPsep(gpsepi, XX, lite = FALSE, nonug = FALSE)a C-side GP object identifier (positive integer);
e.g., as returned by newGP
similar to gpi but indicating a separable GP object,
as returned by newGPsep
a matrix or data.frame containing
a design of predictive locations
a scalar logical indicating whether (lite = FALSE, default) or not
(lite = TRUE) a full predictive covariance matrix should be
returned, as would be required for plotting random sample paths,
but substantially increasing computation time if only point-prediction
is required
a scalar logical indicating if a (nonzero) nugget should be used in the predictive
equations; this allows the user to toggle between visualizations of uncertainty due just
to the mean, and a full quantification of predictive uncertainty. The latter (default nonug = FALSE)
is the standard approach, but the former may work better in some sequential design contexts. See, e.g.,
ieciGP
The output is a list with the following components.
a vector of predictive means of length nrow(Xref)
covariance matrix of
for a multivariate Student-t distribution; alternately
if lite = TRUE,
then a field s2 contains the diagonal of this matrix
a Student-t degrees of freedom scalar (applies to all
XX)
Returns the parameters of Student-t predictive equations. By
default, these include a full predictive covariance matrix between all
XX locations. However, this can be slow when nrow(XX)
is large, so a lite options is provided, which only returns the
diagonal of that matrix.
GP prediction is sometimes called “kriging”, especially in the spatial statistics literature. So this function could also be described as returning evaluations of the “kriging equations”
For standard GP prediction, refer to any graduate text, e.g., Rasmussen & Williams Gaussian Processes for Machine Learning
# NOT RUN {
## a "computer experiment" -- a much smaller version than the one shown
## in the aGP docs
## Simple 2-d test function used in Gramacy & Apley (2015);
## thanks to Lee, Gramacy, Taddy, and others who have used it before
f2d <- function(x, y=NULL)
{
if(is.null(y)) {
if(!is.matrix(x) && !is.data.frame(x)) x <- matrix(x, ncol=2)
y <- x[,2]; x <- x[,1]
}
g <- function(z)
return(exp(-(z-1)^2) + exp(-0.8*(z+1)^2) - 0.05*sin(8*(z+0.1)))
z <- -g(x)*g(y)
}
## design with N=441
x <- seq(-2, 2, length=11)
X <- expand.grid(x, x)
Z <- f2d(X)
## fit a GP
gpi <- newGP(X, Z, d=0.35, g=1/1000)
## predictive grid with NN=400
xx <- seq(-1.9, 1.9, length=20)
XX <- expand.grid(xx, xx)
ZZ <- f2d(XX)
## predict
p <- predGP(gpi, XX, lite=TRUE)
## RMSE: compare to similar experiment in aGP docs
sqrt(mean((p$mean - ZZ)^2))
## visualize the result
par(mfrow=c(1,2))
image(xx, xx, matrix(p$mean, nrow=length(xx)), col=heat.colors(128),
xlab="x1", ylab="x2", main="predictive mean")
image(xx, xx, matrix(p$mean-ZZ, nrow=length(xx)), col=heat.colors(128),
xlab="x1", ylab="x2", main="bas")
## clean up
deleteGP(gpi)
## see the newGP and mleGP docs for examples using lite = FALSE for
## sampling from the joint predictive distribution
# }