timse_optim_parallel {KrigInv}

Parallel targeted IMSE criterion

Description

Evaluation of the "timse" criterion for some candidate points. To be used in optimization routines, like in max_timse_parallel. To avoid numerical instabilities, the new points are evaluated only if they are not too close to an existing observation, or if there is some observation noise. The criterion is the integral of the posterior timse uncertainty.

Usage

timse_optim_parallel(x, integration.points, integration.weights = NULL, 
intpoints.oldmean = NULL, intpoints.oldsd = NULL, 
precalc.data, model, T, new.noise.var = 0, weight = NULL,
batchsize, current.timse)

Arguments

x

Input vector of size d at which one wants to evaluate the criterion.

integration.points

p*d matrix of points for numerical integration in the X space.

integration.weights

Vector of size p corresponding to the weights of these integration points.

intpoints.oldmean

Vector of size p corresponding to the kriging mean at the integration points before adding x to the design of experiments.

intpoints.oldsd

Vector of size p corresponding to the kriging standard deviation at the integration points before adding x to the design of experiments.

precalc.data

List containing useful data to compute quickly the updated kriging variance. This list can be generated using the precomputeUpdateData function.

model

Object of class km (Kriging model).

T

Array containing one or several thresholds.

new.noise.var

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

weight

Vector of weight function (length must be equal to the number of lines of the matrix integration.points). If nothing is set, the imse criterion is used instead of timse. It corresponds to equal weights.

batchsize

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

current.timse

Current value of the timse criterion (before adding new observations)

Value

Targeted imse value

Author(s)

Victor Picheny (INRA, Toulouse, France)

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

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

See Also

EGIparallel, max_timse_parallel

Examples

#timse_optim_parallel

set.seed(9)
N <- 20 #number of observations
T <- c(80,100) #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")

###we need to compute some additional arguments:
#integration points, and current kriging means and variances at these points
integcontrol <- list(n.points=1000,distrib="timse",init.distrib="MC")
obj <- integration_design(integcontrol=integcontrol,lower=c(0,0),
upper=c(1,1),model=model,T=T)

integration.points <- obj$integration.points
integration.weights <- obj$integration.weights
pred <- predict_nobias_km(object=model,newdata=integration.points,
type="UK",se.compute=TRUE)
intpoints.oldmean <- pred$mean ; intpoints.oldsd<-pred$sd

#another precomputation
precalc.data <- precomputeUpdateData(model,integration.points)

#we also need to compute weights. Otherwise the (more simple) 
#imse criterion will be evaluated
weight0 <- 1/sqrt( 2*pi*(intpoints.oldsd^2) )
weight <- 0
for(i in 1:length(T)){
  Ti <- T[i]
  weight <- weight + weight0 * exp(-0.5*((intpoints.oldmean-Ti)/sqrt(intpoints.oldsd^2))^2)
}

batchsize <- 4
x <- c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8)
#one evaluation of the timse_optim_parallel criterion
#we calculate the expectation of the future "timse" 
#uncertainty when 4 points are added to the doe
#the 4 points are (0.1,0.2) , (0.3,0.4), (0.5,0.6), (0.7,0.8)
timse_optim_parallel(x=x,integration.points=integration.points,
          integration.weights=integration.weights,
          intpoints.oldmean=intpoints.oldmean,intpoints.oldsd=intpoints.oldsd,
          precalc.data=precalc.data,T=T,model=model,weight=weight,
          batchsize=batchsize,current.timse=Inf)

#the function max_timse_parallel will help to find the optimum: 
#ie: the batch of 4 minimizing the expectation of the future uncertainty