GADGET (version 0.2.0)

design_experiment: Design Optimal Experiment using Gaussian Process Optimization

Description

This function implements the method by Weaver, et al. (2016) that uses Gaussian process (GP) optimization to estimate an optimal design for a stochastic design criterion. This function can also optimize a deterministic design criterion as well. Validation of the fitted GP models is provided by the statistics described in Bastos and O'Hagan (2009). For sequential physical experiments or computer experiments with an expensive simulator, one can repeatedly use this function to compute the next step's optimal design point. For sequential computer experiments with inexpensive simulators, see sequential_experiment which will automatically run the simulator and continue the sequential design automatically.

Usage

design_experiment(
  criterion,
  lower_bound,
  upper_bound,
  stochastic = TRUE,
  init_budget = 10,
  optim_budget = 10,
  gp_options = list(formula = ~1, kernel = "matern5_2", optimizer = "gen"),
  genoud_options = list(pop.size = 1000, max.generations = 100, wait.generations = 10),
  diagnostics = 1,
  max_augment = 10,
  infile = NULL,
  outfile = NULL,
  verbose = TRUE,
  cluster = NULL
)

Arguments

criterion

A function with vector input of length d (see details).

lower_bound

A vector of length d.

upper_bound

A vector of length d.

stochastic

Is the design criterion stochastic or deterministic (see details)?

init_budget

An integer defining the size of the initial training dataset and the size of the validation dataset for the GP model.

optim_budget

An integer defining the number of GP optimization iterations.

gp_options

A list specifying the type of GP model to fit (see km).

genoud_options

A list specifying the control options to optimizer (see genoud).

diagnostics

Type of GP diagnostics to perform before optimization occurs. There are currently three options: 0 (none), 1 (automatic) a simple Mahalanobis distance significance test, 2 (user inspected) execution is paused for visual inspection of pivoted-Cholesky residuals and QQ-plots.

max_augment

An integer defining the maximum number of design augmentations before terminating GP fitting.

infile

Saved evaluations of the DC from previous GADGET run

outfile

File to save all DC evaluations to while running

verbose

Print extra output during execution?

cluster

A parallel cluster object.

Value

A list containing the optimal design, diagnostic results, and final GP model.

Details

The design criterion (DC) is a stochastic or deterministic univariate function that measures the quality of a proposed design. GADGET assumes the design criterion must be minimized. For example, instead of maximizing the determinant of the Fisher-information matrix, GADGET would minimize the negative determinant of the Fisher-information matrix. If the DC is stochastic then the GP model is fit with a nugget effect and expected quantile improvement (EQI) is used to perform the GP optimization. The optimal design is taken to be the design that maximizes EQI on the final optimization iteration. If the DC is deterministic then the GP model is fit without a nugget effect and expected improvement (EI) is used to perform the optimization. The optimal design is taken to be the design with smallest observed DC over all evaluation of the DC.

The GADGET represents designs as a d-length vector. The user supplied DC function must translate this vector into the apporiate form for computing the DC. The upper_bound and lower_bound arguments define bounds of each element in the vectorized design.

References

Weaver, B. P., Williams, B. J., Anderson-Cook, C. M., Higdon, D. M. (2016). Computational enhancements to Bayesian design of experiments using Gaussian processes. Bayesian Analysis, 11(1), 191<U+2013>213, <doi:10.1214/15-BA945>.

Examples

# NOT RUN {
#--- Deterministic D-Optimal Design ---#
# simple linear regression model
# design = c(x1,x2,p) (two point design with weight) 
# }
# NOT RUN {
dc <- function(design) {
fisher_mat <- (1-design[3])*c(1,design[2]) %*% t(c(1,design[2]))
fisher_mat <- fisher_mat + design[3]*c(1,design[1]) %*% t(c(1,design[1]))
return(-log(det(fisher_mat)))
}
#optim_budget is small for demonstration purposes 
my_result <- design_experiment(dc,
                               c(0,0.5,0),
                               c(0.5,1,1),
                               FALSE,
                               optim_budget = 2) 

#- optimal design -#
print(my_result$experiment)
#- optimization report - #
print(my_result$optimization)
#- final gp model -#
print(my_result$gp)
# }
# NOT RUN {
# }