crit_tMSE: t-MSE criterion

In hetGP: Heteroskedastic Gaussian Process Modeling and Design under Replication

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")

hetGP documentation built on Oct. 3, 2023, 1:07 a.m.