max_vorob_parallel {KrigInv}

Minimizer of the parallel vorob criterion

Description

Minimization, based on the package rgenoud (or on exhaustive search on a discrete set), of the Vorob'ev criterion for a batch of candidate sampling points.

Usage

max_vorob_parallel(lower, upper, optimcontrol = NULL,
batchsize, integration.param, T,
model, new.noise.var = 0,
penalisation = NULL, typeEx = ">")

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. Finally, one can control the field optim.option in order to decide how to optimize the sampling criterion. If optim.option is set to 2 (default), batchsize sequential optimizations in dimension d are performed to find the optimum. If optim.option is set to 1, only one optimization in dimension batchsize*d is performed. This option is only available with "genoud". This option might provide more global and accurate solutions, but is a lot more expensive.

batchsize

Number of points to sample simultaneously. The sampling criterion will return batchsize points at a time for sampling.

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).

T

Target value (scalar). The criterion CANNOT be used with multiple thresholds.

model

A Kriging model of km class.

new.noise.var

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

penalisation

Optional penalization constant for type I errors. If equal to zero, computes the Type II criterion.

typeEx

A character (">" or "<") identifying the type of excursion

Value

A list with components:

par

the best set of parameters found.

value

the value of the Vorob'ev criterion at par.

allvalues

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

Author(s)

Clement Chevalier (University of Neuchatel, Switzerland)

Dario Azzimonti (IDSIA, Switzerland)

References

Chevalier C., Ginsbouger D., Bect J., Molchanov I. (2013) Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with gaussian process models mODa 10, Advances in Model-Oriented Design and Analysis, Contributions to Statistics, pp 35-43

Chevalier C. (2013) Fast uncertainty reduction strategies relying on Gaussian process models Ph.D Thesis, University of Bern

Azzimonti, D., Ginsbourger, D., Chevalier, C., Bect, J., and Richet, Y. (2018). Adaptive design of experiments for conservative estimation of excursion sets. Under revision. Preprint at hal-01379642

See Also

EGIparallel,max_sur_parallel

Examples

#max_vorob_parallel

set.seed(9)
N <- 20 #number of observations
T <- 80 #threshold
testfun <- branin
lower <- c(0,0)
upper <- c(1,1)

#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")

optimcontrol <- list(method="genoud",pop.size=200,optim.option=2)
integcontrol <- list(distrib="timse",n.points=400,init.distrib="MC")
integration.param <- integration_design(integcontrol=integcontrol,d=2,
                                            lower=lower,upper=upper,model=model,
                                            T=T)
batchsize <- 5 #number of new points

## Not run: 
obj <- max_vorob_parallel(lower=lower,upper=upper,optimcontrol=optimcontrol,
                        batchsize=batchsize,T=T,model=model,
                        integration.param=integration.param)
                        #5 optims in dimension 2 !

obj$par;obj$value #optimum in 5 new points
new.model <- update(object=model,newX=obj$par,newy=apply(obj$par,1,testfun),
                       cov.reestim=TRUE)

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

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


## End(Not run)