max_timse: Minimizer of the IMSE or targeted IMSE criterion

Description

Minimization, based on the package rgenoud (or on exhaustive search on a discrete set), of the targeted imse (or imse) criterion.

Usage

max_timse(lower, upper, optimcontrol = NULL, 
integration.param = NULL, T, model, 
new.noise.var = 0, epsilon = 0, imse = FALSE)

Arguments

lower

Vector containing the lower bounds of the design space.

upper

Vector containing the upper bounds of the design space.

optimcontrol

Optional list of control parameters for the optimization of the sampling criterion. The field method defines which optimization method is used: it can be either "genoud" (default) for an optimisation using the genoud algorithm, or "discrete" for an optimisation over a specified discrete set. If the field method is set to "genoud", one can set some parameters of this algorithm: pop.size (default : 50*d), max.generations (10*d), wait.generations (2), BFGSburnin (2) and the mutations P1, P2, up to P9 (see genoud). Numbers into brackets are the default values. If the field method is set to "discrete", one can set the field optim.points: p * d matrix corresponding to the p points where the criterion will be evaluated. If nothing is specified, 100*d points are chosen randomly.

integration.param

Optional list of control parameter for the computation of integrals, containing the fields integration.points: a p*d matrix corresponding to p integrations points and integration.weights: a vector of size p corresponding to the weights of these integration points. If nothing is specified, default values are used (see: function integration_design for more details).

Target value (scalar).

model

A Kriging model of km class.

new.noise.var

Optional scalar value of the noise variance of the new observation.

epsilon

Optional tolerance value (a real positive number). Default value is 0.

imse

Optional boolean to decide if the "imse" criterion should be used instead of "timse". Default: FALSE.

Value

A list with components:

par

the best set of parameters found.

value

the value of the criterion at par.

allvalues

if an optimization on a discrete set of points is chosen, the value of the criterion at all these points

References

Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R.T., Adaptive designs of experiments for accurate approximation of a target region, J. Mech. Des. - July 2010 - Volume 132, Issue 7, http://dx.doi.org/10.1115/1.4001873

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

Chevalier C., Bect J., Ginsbourger D., Vazquez E., Picheny V., Richet Y. (2011), Fast parallel kriging-based stepwise uncertainty reduction with application to the identification of an excursion set ,http://hal.archives-ouvertes.fr/hal-00641108/

Examples

Run this code

# NOT RUN {
#max_timse

set.seed(8)
N <- 9 #number of observations
T <- 80 #threshold
testfun <- branin
lower <- c(0,0)
upper <- c(1,1)

#a 9 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")

optimcontrol <- list(method="genoud",pop.size=50)
integcontrol <- list(distrib="timse",n.points=50,init.distrib="MC")
integration.param <- integration_design(integcontrol=integcontrol,d=2,
                                            lower=lower,upper=upper,model=model,
                                            T=T)

# }
# NOT RUN {
obj <- max_timse(lower=lower,upper=upper,optimcontrol=optimcontrol,T=T,
                model=model,integration.param=integration.param)

obj$par;obj$value
new.model <- update_km(model=model,NewX=obj$par,NewY=testfun(obj$par),
                       CovReEstimate=TRUE)

par(mfrow=c(1,2))
print_uncertainty(model=model,T=T,type="pn",lower=lower,upper=upper,
cex.points=2.5,main="probability of excursion")

print_uncertainty(model=new.model,T=T,type="pn",lower=lower,upper=upper,
new.points=1,col.points.end="red",cex.points=2.5,
main="updated probability of excursion")
# }