dials (version 1.4.1)

grid_space_filling: Space-filling parameter grids

Description

Experimental designs for computer experiments are used to construct parameter grids that try to cover the parameter space such that any portion of the space has does not have an observed combination that is unnecessarily close to any other point.

Usage

grid_space_filling(x, ..., size = 5, type = "any", original = TRUE)
# S3 method for parameters
grid_space_filling(
  x,
  ...,
  size = 5,
  type = "any",
  variogram_range = 0.5,
  iter = 1000,
  original = TRUE
)
# S3 method for list
grid_space_filling(
  x,
  ...,
  size = 5,
  type = "any",
  variogram_range = 0.5,
  iter = 1000,
  original = TRUE
)
# S3 method for param
grid_space_filling(
  x,
  ...,
  size = 5,
  variogram_range = 0.5,
  iter = 1000,
  type = "any",
  original = TRUE
)

Arguments

x

A param object, list, or parameters.

...

One or more param objects (such as mtry() or penalty()). None of the objects can have unknown() values in the parameter ranges or values.

size

A single integer for the maximum number of parameter value combinations returned. If duplicate combinations are generated from this size, the smaller, unique set is returned.

type

A character string with possible values: "any", "audze_eglais", "max_min_l1", "max_min_l2", "uniform", "max_entropy", or "latin_hypercube". A value of "any" will choose the first design available (in the order listed above, excluding "latin_hypercube"). For a single-point design, a random grid is created.

original

A logical: should the parameters be in the original units or in the transformed space (if any)?

variogram_range

A numeric value greater than zero. Larger values reduce the likelihood of empty regions in the parameter space. Only used for type = "max_entropy".

iter

An integer for the maximum number of iterations used to find a good design. Only used for type = "max_entropy".

Details

The types of designs supported here are latin hypercube designs of different types. The simple designs produced by grid_latin_hypercube() are space-filling but don’t guarantee or optimize any other properties. grid_space_filling() might be able to produce designs that discourage grid points from being close to one another. There are a lot of methods for doing this, such as maximizing the minimum distance between points (see Husslage et al 2001). grid_max_entropy() attempts to maximize the determinant of the spatial correlation matrix between coordinates.

Latin hypercube and maximum entropy designs use random numbers to make the designs.

By default, grid_space_filling() will try to use a pre-optimized space-filling design from https://www.spacefillingdesigns.nl/ (see Husslage et al, 2011) or using a uniform design. If no pre-made design is available, then a maximum entropy design is created.

Also note that there may a difference in grids depending on how the function is called. If the call uses the parameter objects directly the possible ranges come from the objects in dials. For example:

mixture()

## Proportion of Lasso Penalty (quantitative)
## Range: [0, 1]

set.seed(283)
mix_grid_1 <- grid_latin_hypercube(mixture(), size = 1000)
range(mix_grid_1$mixture)

## [1] 0.0001530482 0.9999530388

However, in some cases, the parsnip and recipe packages overrides the default ranges for specific models and preprocessing steps. If the grid function uses a parameters object created from a model or recipe, the ranges may have different defaults (specific to those models). Using the example above, the mixture argument above is different for glmnet models:

library(parsnip)
library(tune)
# When used with glmnet, the range is [0.05, 1.00]
glmn_mod <-
  linear_reg(mixture = tune()) |>
  set_engine("glmnet")
set.seed(283)
mix_grid_2 <-
  glmn_mod |> 
  extract_parameter_set_dials() |> 
  grid_latin_hypercube(size = 1000)
range(mix_grid_2$mixture)

## [1] 0.0501454 0.9999554

References

Sacks, Jerome & Welch, William & J. Mitchell, Toby, and Wynn, Henry. (1989). Design and analysis of computer experiments. With comments and a rejoinder by the authors. Statistical Science. 4. 10.1214/ss/1177012413.

Santner, Thomas, Williams, Brian, and Notz, William. (2003). The Design and Analysis of Computer Experiments. Springer.

Dupuy, D., Helbert, C., and Franco, J. (2015). DiceDesign and DiceEval: Two R packages for design and analysis of computer experiments. Journal of Statistical Software, 65(11)

Husslage, B. G., Rennen, G., Van Dam, E. R., & Den Hertog, D. (2011). Space-filling Latin hypercube designs for computer experiments. Optimization and Engineering, 12, 611-630.

Fang, K. T., Lin, D. K., Winker, P., & Zhang, Y. (2000). Uniform design: Theory and application. _Technometric_s, 42(3), 237-248

Examples

grid_space_filling(
  hidden_units(),
  penalty(),
  epochs(),
  activation(),
  learn_rate(c(0, 1), trans = scales::transform_log()),
  size = 10,
  original = FALSE
)
# ------------------------------------------------------------------------------
# comparing methods

if (rlang::is_installed("ggplot2")) {

  library(dplyr)
  library(ggplot2)

  set.seed(383)
  parameters(trees(), mixture()) |>
    grid_space_filling(size = 25, type = "latin_hypercube") |>
    ggplot(aes(trees, mixture)) +
    geom_point() +
    lims(y = 0:1, x = c(1, 2000)) +
    ggtitle("latin hypercube")

  set.seed(383)
  parameters(trees(), mixture()) |>
    grid_space_filling(size = 25, type = "max_entropy") |>
    ggplot(aes(trees, mixture)) +
    geom_point() +
    lims(y = 0:1, x = c(1, 2000)) +
    ggtitle("maximum entropy")

  parameters(trees(), mixture()) |>
    grid_space_filling(size = 25, type = "audze_eglais") |>
    ggplot(aes(trees, mixture)) +
    geom_point() +
    lims(y = 0:1, x = c(1, 2000)) +
    ggtitle("Audze-Eglais")

  parameters(trees(), mixture()) |>
    grid_space_filling(size = 25, type = "uniform") |>
    ggplot(aes(trees, mixture)) +
    geom_point() +
    lims(y = 0:1, x = c(1, 2000)) +
    ggtitle("uniform")
}