svdGP: Full SVD-Based GP Models

In DynamicGP: Modelling and Analysis of Dynamic Computer Experiments

Full SVD-Based GP Models

Description

This function fits a full SVD-based GP model with test set X0, design set design and response matrix resp.

Usage

svdGP(design,resp,X0=design,nstarts=5,gstart=0.0001,
      frac=.95,centralize=FALSE,nthread=1,clutype="PSOCK")

Arguments

design	An N by d matrix of N training/design inputs.
resp	An L by N response matrix of design, where L is the length of the time series outputs, N is the number of design points.
X0	An M by d matrix of M test inputs. The default value of X0 is design.
nstarts	The number of starting points used in the numerical maximization of the posterior density function. The larger nstarts will typically lead to more accurate prediction but longer computational time. The default value is 5.
gstart	The starting number and upper bound for estimating the nugget parameter. If gstart = sqrt(.Machine$double.eps), the nugget parameter will be fixed at sqrt(.Machine$double.eps), since sqrt(.Machine$double.eps) is the lower bound of the nugget term. The default value is 0.0001.
frac	The threshold in the cumulative percentage criterion to select the number of SVD bases. The default value is 0.95.
centralize	If centralize=TRUE the response matrix will be centralized (subtract the mean) before the start of the algorithm. The mean will be added to the predictive mean at the finish of the algorithm. The default value is FALSE.
nthread	The number of threads (processes) used in parallel execution of this function. nthread=1 implies no parallelization. The default value is 1.
clutype	The type of cluster in the R package "parallel" to perform parallelization. The default value is "PSOCK". Required only if nthread>1.

Value

pmean	An L by M matrix of posterior predicted mean for the response at the test set X0.
ps2	An L by M matrix of posterior predicted variance for the response at the test set X0.

Author(s)

Ru Zhang [e-mail],

C. Devon Lin [e-mail],

Pritam Ranjan [e-mail]

See Also

knnsvdGP, lasvdGP.

Examples

library("lhs")
forretal <- function(x,t,shift=1)
{
    par1 <- x[1]*6+4
    par2 <- x[2]*16+4
    par3 <- x[3]*6+1
    t <- t+shift
    y <- (par1*t-2)^2*sin(par2*t-par3)
}
timepoints <- seq(0,1,len=200)
design <- lhs::randomLHS(50,3)
test <- lhs::randomLHS(50,3)

## evaluate the response matrix on the design matrix
resp <- apply(design,1,forretal,timepoints)

## fit full SVD-based GP model
ret <- svdGP(design,resp,test,frac=.95,nstarts=1,
             centralize=TRUE,nthread=2)

DynamicGP documentation built on Nov. 10, 2022, 5:15 p.m.