Score candidate experiments with expected improvement

Calculates expected improvement for one or more candidate rows. Higher values indicate candidates that offer a better combination of predicted improvement and uncertainty.

Usage

magp_expected_improvement(
  object,
  newdata,
  direction = c("minimize", "maximize"),
  best = NULL,
  xi = 0
)

Arguments

object

A fitted magp2d or magpfull model.

newdata

A numeric matrix or data frame accepted by the model's stats::predict() method.

direction

Use "minimize" when smaller responses are better and "maximize" when larger responses are better.

best

Optional response that a new point should improve upon. When it is omitted, the function uses the best observed response in object.

xi

Nonnegative improvement offset. The default is 0. Larger values require a candidate to exceed best by more.

Value

A nonnegative numeric vector with one expected-improvement value per row of newdata.

Details

Expected improvement uses the model's latent predictive mean and standard error. A candidate can receive a high value because its predicted response is good, its uncertainty is large, or both. Rows already present in the training data receive a value of zero. Predictions with variance below 1e-8 also receive zero.

References

Jones, D. R., Schonlau, M., and Welch, W. J. (1998). Efficient Global Optimization of Expensive Black-Box Functions. Journal of Global Optimization, 13, 455-492. doi:10.1023/A:1008306431147 .

Examples

# \donttest{
train <- read.table(
  system.file("extdata", "example_train.txt", package = "magp"),
  header = TRUE
)
test <- read.table(
  system.file("extdata", "example_test.txt", package = "magp"),
  header = TRUE
)
fit <- magp2d_fit(train, seed = 1)
magp_expected_improvement(
  fit,
  test[1:3, ],
  direction = "minimize"
)
#> [1] 1.0641766 0.5910628 2.1282648
# }