max_futureVol_parallel {KrigInv}

Maximize parallel volume criterion

Description

Maximizes the criterion vorobVol_optim_parallel.

Usage

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

Arguments

lower

lower bounds of the domain

upper

upper bounds of the domain

optimcontrol

optional list of control parameters for optimization aspects, see max_vorob_parallel for details

batchsize

size of the batch of new points

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

threshold

model

a km Model

new.noise.var

Optional scalar with the noise variance at the new observation

typeEx

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

Value

A list containing par, the best set of parameters found, value the value of the criterion and alpha, the Vorob'ev quantile corresponding to the conservative estimate.

Author(s)

Dario Azzimonti (IDSIA, Switzerland)

References

Azzimonti, D. and Ginsbourger, D. (2018). Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimation. Journal of Computational and Graphical Statistics, 27(2), 255-267.

Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD 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

Chevalier, C., Bect, J., Ginsbourger, D., Vazquez, E., Picheny, V., and Richet, Y. (2014). Fast kriging-based stepwise uncertainty reduction with application to the identification of an excursion set. Technometrics, 56(4):455-465.

See Also

EGIparallel,max_vorob_parallel

Examples

#max_futureVol_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_futureVol_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)

  consLevel = 0.95; n_discrete_design=500*new.model@d
  CE_design=as.matrix (randtoolbox::sobol (n = n_discrete_design,
                              dim = new.model@d))
  colnames(CE_design) <- colnames(new.model@X)
  current.pred = predict.km(object = new.model,
                            newdata = CE_design,
                            type = "UK",cov.compute = TRUE)
  current.pred$cov <- current.pred$cov +1e-7*diag(nrow = nrow(current.pred$cov),
                                                  ncol = ncol(current.pred$cov))

  current.CE = anMC::conservativeEstimate(alpha = consLevel, pred=current.pred,
                                    design=CE_design, threshold=T, pn = NULL,
                                    type = ">", verb = 1,
                                    lightReturn = TRUE, algo = "GANMC")

  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",consQuantile=obj$alpha)

  print_uncertainty(model=new.model,T=T,type="pn",lower=lower,upper=upper,
                    new.points=batchsize,col.points.end="red",cex.points=2.5,
                    main="updated probability of excursion",consQuantile=current.CE$lvs)


## End(Not run)