tmse_optim {KrigInv}

Targeted MSE criterion

Description

Evaluation of the Targeted MSE criterion. To be used in optimization routines, like in max_infill_criterion

Usage

tmse_optim(x, model, T, method.param = NULL)

Arguments

x

Input vector at which one wants to evaluate the criterion. This argument can be either a vector of size d (for an evaluation at a single point) or a p*d matrix (for p simultaneous evaluations of the criterion at p different points).

model

An object of class km (Kriging model).

T

Array containing one or several thresholds.

method.param

Scalar tolerance around the targets T.

Value

targeted MSE value. When the argument x is a vector the function returns a scalar. When the argument x is a p*d matrix the function returns a vector of size p.

Author(s)

Victor Picheny (INRA, Toulouse, France)

David Ginsbourger (IDIAP Martigny and University of Bern, Switzerland)

Clement Chevalier (University of Neuchatel, Switzerland)

References

Picheny V., Ginsbourger D., Roustant O., Haftka R.T., (2010) Adaptive designs of experiments for accurate approximation of a target region, J. Mech. Des. vol. 132(7)

Picheny V. (2009) Improving accuracy and compensating for uncertainty in surrogate modeling, Ph.D. thesis, University of Florida and Ecole Nationale Superieure des Mines de Saint-Etienne

See Also

EGI, max_infill_criterion

Examples

#tmse_optim

set.seed(9)
N <- 20 #number of observations
T <- c(40,80) #thresholds
testfun <- branin

#a 20 points initial design
design <- data.frame( matrix(runif(2*N),ncol=2) )
response <- testfun(design)

#km object with matern3_2 covariance
#params estimated by ML from the observations
model <- km(formula=~., design = design, 
	response = response,covtype="matern3_2")

x <- c(0.5,0.4)#one evaluation of the tmse criterion
tmse_optim(x=x,T=T,model=model)

n.grid <- 20 #you can run it with 100
x.grid <- y.grid <- seq(0,1,length=n.grid)
x <- expand.grid(x.grid, y.grid)
tmse.grid <- tmse_optim(x=x,T=T,model=model)
z.grid <- matrix(tmse.grid, n.grid, n.grid)

#plots: contour of the criterion, doe points and new point
image(x=x.grid,y=y.grid,z=z.grid,col=grey.colors(10))
contour(x=x.grid,y=y.grid,z=z.grid,25,add=TRUE)
points(design, col="black", pch=17, lwd=4,cex=2)

i.best <- which.max(tmse.grid)
points(x[i.best,], col="blue", pch=17, lwd=4,cex=3)

#plots the real (unknown in practice) curve f(x)=T
testfun.grid <- apply(x,1,testfun)
z.grid.2 <- matrix(testfun.grid, n.grid, n.grid)
contour(x.grid,y.grid,z.grid.2,levels=T,col="blue",add=TRUE,lwd=5)
title("Contour lines of tmse criterion (black) and of f(x)=T (blue)")