findQ: Main solver
In vpicheny/quantile: Quantile estimation

Description Usage Arguments Details Value Author(s) References Examples

View source: R/findQ.R

Main function to find quantiles.

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findQ(model, fun, alpha = 0.95, n.ite = 45, n = 1000, n.large = NULL,
  n.cluster = 1, seed = 42, n.candidates = NULL, Xdistrib = NULL,
  x = NULL, cov.reestim = TRUE)

`model`	an object of class km
`fun`	the function of interest
`alpha`	the quantile level
`n.ite`	number of iterations (points to add)
`n`	the number of points used for integration
`n.large`	(optional) a larger number of points used prior to integration
`n.cluster`	number of cores used (requires the libraries `forreach` and `doparallel`)
`seed`	the seed
`n.candidates`	(optional) a smaller number of candidate points on which the criterion is computed
`Xdistrib, x`	`Xdistrib` is a function that returns a sample of x given an integer, and x is a matrix (see details)
`cov.reestim`	Boolean; if TRUE, the GP parameters are re-estimated at each iteration

Either the distribution of the input Xdistrib or a sample x must be given. If x is given, the problem is treated as discrete.

In the standard setting, a large number of points (n.large) is generated using Xdistrib, out of which n useful integration points are selected. The SUR criterion is then evaluated at the most promising n.candidates points. Finally, a local optimization is performed using BFGS from the best candidate.

Maximum recommended values are 5,000 for n, 1e6 for n.large and 1,000 for n.candidates.

A list with all.qn (all the quantiles estimated) and model (the last km model)

Victor Picheny

T. Labopin-Richard, V. Picheny, "Sequential design of experiments for estimating quantiles of black-box functions", Statistica Sinica, 2017, doi:10.5705/ss.202016.0160

## Not run: 
library(DiceDesign)
#--------------------------------------------------------#
# Set problem parameters
fun <- branin
d <- 2
n.init <- 6
n.ite <- 24
seed <- 42
n <- 2e3
#--------------------------------------------------------#
# Define distribution over the input X
mu <- rep(.5, d)
Sigma <- matrix(rep(.05, d*d), d,d)
diag(Sigma) <- .1
Xdistrib <- function(n) return(mvrnorm(n=n, mu=mu, Sigma))
#--------------------------------------------------------#
# Initial set of observations (rescaled to fit Xdistrib)
x.init <- lhsDesign(n.init, d, seed=seed)$design
x.init <- mu + qnorm(x.init) %*% chol(Sigma)
y.init <- as.numeric(apply(x.init, 1, fun))
#--------------------------------------------------------#
# Initial kriging model
model <- km(~., design=data.frame(x=x.init), response=y.init, 
            lower=rep(.05,d), upper=rep(1,d), control=list(trace=FALSE))
#--------------------------------------------------------#
# Sequential design
res <- findQ(model=model, fun=fun, alpha=.95, n.ite=n.ite, n=n, n.cluster=1, seed=seed, n.large=1e5,
             n.candidates=100, Xdistrib=Xdistrib, cov.reestim = TRUE)
#--------------------------------------------------------#
# Plot DoE and quantile estimates
plot(res$model@X[,1], res$model@X[,2])
plot(res$all.qn)

## End(Not run)