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Evaluate Wasserstein-Bures approximation of the Optimal Transport solution

Source: R/ot_indices_bw.R
ot_indices_wb.Rd

Evaluate Wasserstein-Bures approximation of the Optimal Transport solution

Usage

ot_indices_wb(
  x,
  y,
  M,
  boot = FALSE,
  R = NULL,
  parallel = "no",
  ncpus = 1,
  conf = 0.95,
  type = "norm"
)

Arguments

x

A matrix or data.frame containing the input(s) values. The values can be numeric, factors, or strings. The type of data changes the partitioning. If the values are continuous (double), the function partitions the data into M sets. If the values are discrete (integers, strings, factors), the number of partitioning sets is data-driven.

y

A matrix containing the output values. Each column represents a different output variable, and each row represents a different observation. Only numeric values are allowed.

M

A scalar representing the number of partitions for continuous inputs.

boot

(default FALSE) Logical that sets whether or not to perform bootstrapping of the OT indices.

R

(default NULL) Positive integer, number of bootstrap replicas.

parallel

(default "no") The type of parallel operation to be used (if any). If missing, the default is taken from the option boot.parallel (and if that is not set, "no"). Only considered if boot = TRUE. For more information, check the boot::boot() function.

ncpus

(default 1) Positive integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs. Check the ncpus option in the boot::boot() function of the boot package.

conf

(default 0.95) Number between 0 and 1 representing the confidence level. Only considered if boot = TRUE.

type

(default "norm") Method to compute the confidence interval. Only considered if boot = TRUE. For more information, check the type option of boot::boot.ci().

Value

A gsaot_indices object containing:

  • method: a string that identifies the type of indices computed.

  • indices: a names array containing the sensitivity indices between 0 and 1 for each column in x, indicating the influence of each input variable on the output variables.

  • bound: a double representing the upper bound of the separation measure or an array representing the mean of the separation for each input according to the bootstrap replicas.

  • x, y: input and output data provided as arguments of the function.

  • inner_statistic: a list of matrices containing the values of the inner statistics for the partitions defined by partitions. If method = wasserstein-bures, each matrix has three rows containing the Wasserstein-Bures indices, the Advective, and the Diffusive components.

  • partitions: a matrix containing the partitions built to calculate the sensitivity indices. Each column contains the partition associated to the same column in x. If boot = TRUE, the object contains also:

  • indices_ci: a data.frame with first column the input, second and third columns the lower and upper bound of the confidence interval.

  • inner_statistic_ci: a list of matrices. Each element of the list contains the lower and upper confidence bounds for the partition defined by the row.

  • bound_ci: a list containing the lower and upper bounds of the confidence intervals of the separation measure bound.

  • type, conf: type of confidence interval and confidence level, provided as arguments.

See also

ot_indices(), ot_indices_1d()

Examples

N <- 1000

mx <- c(1, 1, 1)
Sigmax <- matrix(data = c(1, 0.5, 0.5, 0.5, 1, 0.5, 0.5, 0.5, 1), nrow = 3)

x1 <- rnorm(N)
x2 <- rnorm(N)
x3 <- rnorm(N)

x <- cbind(x1, x2, x3)
x <- mx + x %*% chol(Sigmax)

A <- matrix(data = c(4, -2, 1, 2, 5, -1), nrow = 2, byrow = TRUE)
y <- t(A %*% t(x))

x <- data.frame(x)
y <- y

ot_indices_wb(x, y, 100)
#> Method: wasserstein-bures 
#> 
#> Indices:
#>        X1        X2        X3 
#> 0.5270767 0.5380900 0.1831289 
#> 
#> Advective component:
#>        X1        X2        X3 
#> 0.3143543 0.3362151 0.1423724 
#> 
#> Diffusive component:
#>         X1         X2         X3 
#> 0.21272243 0.20187498 0.04075641 
#> 
#> Upper bound: 92.57906