GloptiPolyRegion: Confidence region for optima of up to cubic polynomial models...

In PengChenEngineer/OptimaRegion: Confidence Regions for Optima

Description

Computes and displays an approximated (1 - alpha) confidence region (CR) for the bound-constrained maximum of a polynomial regression model in up to cubic order with up to 5 controllable factors \insertCiteDelCastilloCROptimaRegion.

Usage

GloptiPolyRegion(X, y, degree, lb, ub, B = 200, alpha = 0.05,
  maximization = TRUE, verbose = TRUE)

Arguments

X	numeric matrix of shape (N, k); N is the sample size; k is the number of variables, which can be 2, 3, 4 and 5; X specifies the design matrix
y	numeric vector of shape (N, 1); y specifies the responses
degree	integer scalor; degree specifies the order of the polynomial model, which can be 2 or 3
lb	numeric vector of shape (1, k); lb specifies the lower bounds for the k variables
ub	numeric vector of shape (1, k); ub specifies the upper bounds for the k variables
B	integer scalor; B specifies the number of bootstrap operations
alpha	numeric scalor between 0 and 1; alpha specifies the nominal confidence level, 1 - alpha, of the confidence region
maximization	boolean scalor; if specifies whether the algorithm computes the confidence region for the maxima or minima
verbose	boolean scalor; it specifies whether to display running status
axes_labels	vector of strings; it specifies the name of each experimental factor to be displayed on the CR plot; the default value is NULL, when the labels will be set to x1, x2, ...

Value

Upon completion, a figure displaying the confidence region of the true optimum projected onto each pairwise-variable planes will be created (a pdf file will also be generated), and the function also returns a list consisting of 2 components:

boot_optima

numeric matrix of shape ((1 - alpha)B, k); it contains the (1 - alpha)B bootstrap optima

bagged_optimum

numeric vector of shape (1, k); the bagged optimum; computed by taking the column average of boot_optima

Author(s)

Enrique del Castillo [e-mail], Peng Chen [e-mail], Adam Meyers [e-mail], John Hunt [e-mail] and James Rapkin [e-mail].

References

\insertAllCited

Examples

## Not run: 
# Example 1: run GloptiPolyRegion on a quadratic, 3 vars example
out <- GloptiPolyRegion(
  X = quad_3D[, 1:3], y = quad_3D[, 4], degree = 2,
  lb = c(-2, -2, -2), ub = c(2, 2, 2), B = 500, alpha = 0.1,
  maximization = TRUE, verbose = TRUE)
plot(out, c("x1", "x2", "x3"))

# Example 2: run GloptiPolyRegion on a cubic, 5 vars example
out <- GloptiPolyRegion(
  X = cubic_5D$design_matrix, y = cubic_5D$response,
  degree = 3, lb = rep(0, 5), ub = rep(5, 5), B = 200,
  alpha = 0.05, maximization = TRUE, verbose = TRUE)
plot(out, c("x1", "x2", "x3", "x4", "x5"))

## End(Not run)

PengChenEngineer/OptimaRegion documentation built on Jan. 7, 2020, 9:49 a.m.