crit_tMSE {hetGP}

t-MSE criterion

Description

Computes targeted mean squared error infill criterion

Usage

crit_tMSE(x, model, thres = 0, preds = NULL, seps = 0.05)

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

preds

optional predictions at x to avoid recomputing if already done (must contain cov)

seps

parameter for the target window

References

Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R., Kim, N. (2010). Adaptive designs of experiments for accurate approximation of a target region, Journal of Mechanical Design (132), p. 071008.

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 <- 101; 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))

critgrid <- apply(Xgrid, 1, crit_tMSE, model = model)

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