optim_pn_MC: Maximizing excursion probabilities by sampling uniformly...
In IRSN/RobustInv: "Robust inversion of expensive black-box functions"

Description Usage Arguments Value Author(s) Examples

Computes or maximizes excursion probability of points in Dinv based on either a fixed matrix of simulation points in D or on a Monte-Carlo optimization procedure.

1 2	optim_pn_MC(inv.integration.points, model, T, opt.index, inv.index, lower, upper, n.optpoints, pop.size, MC = TRUE, deterministicMat = NULL)

`inv.integration.points`	Matrix of dimension n x dinv where n is the number of integration points and dinv the number of controlled parameters.
`model`	The current kriging model. km object.
`T`	Target threshold.
`opt.index`	Array with integers corresponding to the indices of the nuisance parameters.
`inv.index`	Array with integers corresponding to the indices of the controlled parameters.
`lower`	Array of size d. Lower bound of the input domain.
`upper`	Array of size d. Upper bound of the input domain.
`n.optpoints`	The number of simulation points in Dopt. Multivariate integrals in dimension `n.optpoints` are performed, so no value larger than 10 should be used.
`pop.size`	The number of Monte-Carlo samples used to maximize the excursion probability. Does not apply if `MC = FALSE`.
`MC`	Boolean. Is Monte-Carlo optimization required ?
`deterministicMat`	Applies only if `MC = FALSE`. Matrix of dimension (n*p) x d containing the simulation points used to compute (only once) pn through a multivariate integral.

A list with the following fields. (i) integration.points: (n*p) x d matrix containing the simulation points optimizing the excursion probability. First p rows are associated to integration point 1, and so on. (ii) cov: (n*p) x p matrix containing the n different non-conditional covariance matrix in each batch of p points selected by the optimization procedure. (iii) mean: Array of size n*p with the kriging means of the simulation points. (iv) pn: Array of size n with the (underestimated) excursion probabilities for each integration point.

Clement Chevalier clement.chevalier@unine.ch

library(KrigInv)
library(mnormt)
library(randtoolbox)
myfun <- branin_robinv
d <- 3

set.seed(8)

n0 <- 30
T <- 10
opt.index <- c(3)
inv.index <- c(1,2)
lower <- rep(0,times=d)
upper <- rep(1,times=d)
d.inv <- length(inv.index);d.opt <- length(opt.index)
lower.inv <- lower[inv.index];upper.inv <- upper[inv.index]
lower.opt <- lower[opt.index];upper.opt <- upper[opt.index]

design <- matrix(runif(d*n0),nrow=n0)
response <- myfun(design)
model <- km(formula = ~1,design = design,response = response,covtype = "matern3_2")

n <- n.points <- 50 # number of integration points
inv.integration.points <- t(lower.inv + t(sobol(n=n.points,dim=d.inv))*(upper.inv-lower.inv))

p <- n.optpoints <- 2
pop.size <- 20
## Not run: 
result <- optim_pn_MC(inv.integration.points=inv.integration.points,model=model,T=T,
                      opt.index=opt.index,inv.index=inv.index,lower=lower,upper=upper,
                      n.optpoints=n.optpoints,pop.size=pop.size,MC=TRUE)

## End(Not run)
# an example with no MC
opt.simulation.points <- t(lower.opt + t(sobol(n=n.optpoints,dim=d.opt))*(upper.opt-lower.opt))
fullpoints <- matrix(c(0),nrow=n*p , ncol=d)
indices <- expand.grid(c(1:p),c(1:n)) 
index1 <- indices[,1]
index2 <- indices[,2]
fullpoints[,opt.index] <- opt.simulation.points[index1,]
fullpoints[,inv.index] <- inv.integration.points[index2,]
## Not run: 
result2 <- optim_pn_MC(inv.integration.points=inv.integration.points,model=model,T=T,
                       opt.index=opt.index,inv.index=inv.index,lower=lower,upper=upper,
                       n.optpoints=n.optpoints,pop.size=1,MC=FALSE,
                       deterministicMat = fullpoints)

## End(Not run)