crit_ICU {hetGP}

Integrated Contour Uncertainty criterion

Description

Computes ICU infill criterion

Usage

crit_ICU(x, model, thres = 0, Xref, w = NULL, preds = NULL, kxprime = NULL)

Arguments

x

matrix of new designs, one point per row (size n x d)

model

homGP or hetGP model, including inverse matrices

thres

for contour finding

Xref

matrix of input locations to approximate the integral by a sum

w

optional weights vector of weights for Xref locations

preds

optional predictions at Xref to avoid recomputing if already done

kxprime

optional covariance matrix between model$X0 and Xref to avoid its recomputation

References

Lyu, X., Binois, M. & Ludkovski, M. (2018+). Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation. arXiv:1807.06712.

Examples

## Infill criterion example
set.seed(42)
branin <- function(x){
  m <- 54.8104; s <- 51.9496
  if(is.null(dim(x))) x <- matrix(x, nrow = 1)
  xx <- 15 * x[,1] - 5; y <- 15 * x[,2]
  f <- (y - 5.1 * xx^2/(4 * pi^2) + 5 * xx/pi - 6)^2 + 10 * (1 - 1/(8 * pi)) * cos(xx) + 10
  f <- (f - m)/s
  return(f)
}

ftest <- function(x, sd = 0.1){
  if(is.null(dim(x))) x <- matrix(x, nrow = 1)
  return(apply(x, 1, branin) + rnorm(nrow(x), sd = sd))
}

ngrid <- 51; xgrid <- seq(0, 1, length.out = ngrid)
Xgrid <- as.matrix(expand.grid(xgrid, xgrid))
Zgrid <- ftest(Xgrid)

n <- 20
N <- 500
X <- Xgrid[sample(1:nrow(Xgrid), n),]
X <- X[sample(1:n, N, replace = TRUE),]
Z <- ftest(X)
model <- mleHetGP(X, Z, lower = rep(0.001,2), upper = rep(1,2))

# Precalculations for speedup
preds <- predict(model, x = Xgrid)
kxprime <- cov_gen(X1 = model$X0, X2 = Xgrid, theta = model$theta, type = model$covtype)
 
critgrid <- apply(Xgrid, 1, crit_ICU, model = model, Xref = Xgrid,
                  preds = preds, kxprime = kxprime)

filled.contour(matrix(critgrid, ngrid), color.palette = terrain.colors, main = "ICU criterion")