Sequential algorithms to generate designs that fill the output space.

Description

Sequential algorithms to generate a design that produces points filling the output space. The underlying mapping f from input space to output space is assumed to be a black-box function that can be evaluated in the forward direction. Please see Wang et al. (2024) and Wang & Joseph (2025) for details.

Author(s)

Shangkun Wang, V. Roshan Joseph

Maintainer: Shangkun Wang <sk_wang@gatech.edu>

References

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024), "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Wang, Shangkun, and V. Roshan Joseph. (2025), "Comment: A Model-free Method for Input-Output Space-Filling Design." Technometrics, to appear.

Input-Output Space-Filling Design

Description

This function is for producing designs that explicitly balance the input and output points.

Usage

IOSFD(
  D = NULL,
  f,
  p,
  q,
  lambda = 0.5,
  n_ini = NA,
  n,
  scale = TRUE,
  CAND = NULL,
  rand_out = FALSE,
  rand_in = FALSE
)

Arguments

Details

IOSFD produces a design that balances the input and output points by Wang et al. (2025).

Value

References

Wang, Shangkun, and V. Roshan Joseph. (2025), "Comment: A Model-free Method for Input-Output Space-Filling Design." Technometrics, to appear.

Examples

# test function: inverse-radius function (Wang et.al 2023)
inverse_r = function(x){
epsilon = 0.1
y1 = 1 / (x[1]^2 + x[2]^2 + epsilon^2) ^ (1/2)
if (x[2]==0){
 y2 = 0
}else if (x[1]==0) {
  y2 = pi / 2}else{
    y2 = atan(x[2] / x[1])
  }
return (c(y1=y1, y2=y2))
}

set.seed(2022)
p = 2
q = 2
f = inverse_r
n_ini = 10
n = 50
iosfd = IOSFD(f=f, p=p, q=q, n_ini=n_ini, n=n)
D = iosfd$D
Y = iosfd$Y
 

Output Space-Filling Design

Description

This function is for producing designs that fill the output space.

Usage

OSFD(
  D = NULL,
  f,
  p,
  q,
  n_ini = NA,
  n,
  scale = TRUE,
  method = "EI",
  CAND = NULL,
  rand_out = FALSE,
  rand_in = FALSE
)

Arguments

Details

OSFD produces a design that fills the output space using the sequential algorithm by Wang et al. (2024).

Value

References

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024), "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Examples

# test function: inverse-radius function (Wang et.al 2024)
inverse_r = function(x){
epsilon = 0.1
y1 = 1 / (x[1]^2 + x[2]^2 + epsilon^2) ^ (1/2)
if (x[2]==0){
 y2 = 0
}else if (x[1]==0) {
  y2 = pi / 2}else{
    y2 = atan(x[2] / x[1])
  }
return (c(y1=y1, y2=y2))
}

set.seed(2022)
p = 2
q = 2
f = inverse_r
n_ini = 10
n = 50
osfd = OSFD(f=f, p=p, q=q, n_ini=n_ini, n=n)
D = osfd$D
Y = osfd$Y

(Quasi) uniform points in a p-dimensional ball

Description

ball_unif generates random or quasi-random uniform points in a p-dimensional ball.

Usage

ball_unif(cen, rad, n, rand = TRUE)

Arguments

Details

ball_unif generates random uniform points or quasi uniform points by twinning algorithm in a p-dimensional ball.

Value

a matrix of the generated points.

References

Vakayil, Akhil, and V. Roshan Joseph. (2022). "Data twinning". Statistical Analysis and Data Mining: The ASA Data Science Journal, 15(5), 598-610.

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024), "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Examples

x = ball_unif(c(0,0), 1, 10, rand=FALSE)
plot(x, type='p')

Minimax distance

Description

mMdist computes the minimax distance of a deisng in a specified region. A large uniform sample from the specified region is needed to compute the minimax distance.

Usage

mMdist(X, X_space)

Arguments

Details

mMdist approximates the minimax distance of a set of points X by the large sample X_space in the space of interest.

Value

the minimax distance.

References

Johnson, Mark E., Leslie M. Moore, and Donald Ylvisaker. (1990), "Minimax and Maximin Distance Designs”, Journal of Statistical Planning and Inference, 26, 131–148.

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024), "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Examples

# the minimax distance of a random Latin hypercube design
D = randomLHS(5, 2)
mMdist(D, replicate(2, runif(1e5)))

Generate points to approximate the space spanned by the existing points

Description

spanfill generates points to approximate a space based on existing points. These approximate points can be used to find local fill distance in the space or be used as candidate points in active learning.

Usage

spanfill(X, bound = FALSE)

Arguments

Details

spanfill generates points to approximate the space spanned by the existing points. Details can be found in Wang et al. (2024).

Value

a matrix of the generated points to approximate the space.

References

Wang, Shangkun, Adam P. Generale, Surya R. Kalidindi, and V. Roshan Joseph. (2024). "Sequential designs for filling output spaces", Technometrics, 66, 65–76.

Examples

X = matrix(runif(20), ncol=2)
spanfill_points = spanfill(X)
plot(spanfill_points, type='p')