laGP (version 1.5-9)

predGP: GP Prediction/Kriging

Description

Perform Gaussian processes prediction (under isotropic or separable formulation) at new XX locations using a GP object stored on the C-side

Usage

predGP(gpi, XX, lite = FALSE, nonug = FALSE)
predGPsep(gpsepi, XX, lite = FALSE, nonug = FALSE)

Value

The output is a list with the following components.

mean

a vector of predictive means of length nrow(Xref)

Sigma

covariance matrix for a multivariate Student-t distribution; alternately if lite = TRUE, then a field s2 contains the diagonal of this matrix

df

a Student-t degrees of freedom scalar (applies to all XX)

Arguments

gpi

a C-side GP object identifier (positive integer); e.g., as returned by newGP

gpsepi

similar to gpi but indicating a separable GP object, as returned by newGPsep

XX

a matrix or data.frame containing a design of predictive locations

lite

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

nonug

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

Author

Robert B. Gramacy

Details

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”

References

For standard GP prediction, refer to any graduate text, e.g., Rasmussen & Williams Gaussian Processes for Machine Learning, or

Gramacy, R. B. (2020) Surrogates: Gaussian Process Modeling, Design and Optimization for the Applied Sciences. Boca Raton, Florida: Chapman Hall/CRC. (See Chapter 5.) https://bobby.gramacy.com/surrogates/

See Also

vignette("laGP"), newGP, mleGP, jmleGP,

Examples

## 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