crit_MCU {hetGP}

Maximum Contour Uncertainty criterion

Description

Computes MCU infill criterion

Usage

crit_MCU(x, model, thres = 0, gamma = 2, preds = 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

gamma

optional weight in -|f(x) - thres| + gamma * s(x). Default to 2.

preds

optional predictions at x to avoid recomputing if already done

References

Srinivas, N., Krause, A., Kakade, S, & Seeger, M. (2012). Information-theoretic regret bounds for Gaussian process optimization in the bandit setting, IEEE Transactions on Information Theory, 58, pp. 3250-3265.

Bogunovic, J., Scarlett, J., Krause, A. & Cevher, V. (2016). Truncated variance reduction: A unified approach to Bayesian optimization and level-set estimation, in Advances in neural information processing systems, pp. 1507-1515.

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_MCU, model = model)

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