Co-variation matrices

Construction of model-preserving co-variation matrices for objects of class CI.

Usage

total_covar_matrix(ci, entry, delta)

col_covar_matrix(ci, entry, delta)

partial_covar_matrix(ci, entry, delta)

row_covar_matrix(ci, entry, delta)

Arguments

ci

object of class CI.

entry

a vector of length two specifying the entry of the covariance matrix to vary.

delta

multiplicative variation coefficient for the entry of the covariance matrix given in entry.

Value

A co-variation matrix of the same size of the covariance matrix of CI.

Details

Functions to compute total, partial, row-based and column-based co-variation matrices to ensure the conditional independences of the original Bayesian network hold after a variation. If no co-variation is required for model-preservation the functions return a matrix filled with ones (no co-variation).

References

C. Görgen & M. Leonelli (2020), Model-preserving sensitivity analysis for families of Gaussian distributions. Journal of Machine Learning Research, 21: 1-32.

See also

model_pres_cov

Examples

total_covar_matrix(synthetic_ci,c(1,1),0.3)
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    1    1    1
#> [2,]    1    1    1    1
#> [3,]    1    1    1    1
#> [4,]    1    1    1    1
total_covar_matrix(synthetic_ci,c(1,2),0.3)
#>      [,1] [,2] [,3] [,4]
#> [1,]  0.3  1.0  0.3  0.3
#> [2,]  1.0  0.3  0.3  0.3
#> [3,]  0.3  0.3  0.3  0.3
#> [4,]  0.3  0.3  0.3  0.3
partial_covar_matrix(synthetic_ci,c(1,2),0.3)
#>      [,1] [,2] [,3] [,4]
#> [1,]  1.0  1.0  0.3    1
#> [2,]  1.0  0.3  0.3    1
#> [3,]  0.3  0.3  1.0    1
#> [4,]  1.0  1.0  1.0    1
row_covar_matrix(synthetic_ci,c(1,2),0.3)
#>      [,1] [,2] [,3] [,4]
#> [1,]    1  1.0    1    1
#> [2,]    1  0.3    1    1
#> [3,]    1  1.0    1    1
#> [4,]    1  1.0    1    1
col_covar_matrix(synthetic_ci,c(1,2),0.3)
#>      [,1] [,2] [,3] [,4]
#> [1,]  1.0    1  0.3    1
#> [2,]  1.0    1  1.0    1
#> [3,]  0.3    1  1.0    1
#> [4,]  1.0    1  1.0    1