Frobenius norm for CI — Fro.CI • bnmonitor

Fro.CI returns the Frobenius norm between an object of class CI and its update after a model-preserving parameter variation.

Usage

# S3 method for CI
Fro(x, type, entry, delta, log = TRUE, ...)

Arguments

x: object of class CI.
type: character string. Type of model-preserving co-variation: either "total", "partial", row, column or all. If all the Frobenius norm is computed for every type of co-variation matrix.
entry: a vector of length 2 indicating the entry of the covariance matrix to vary.
delta: numeric vector with positive elements, including the variation parameters that act multiplicatively.
log: boolean value. If TRUE, the logarithm of the Frobenius norm is returned. Set by default to TRUE.
...: additional arguments for compatibility.

Value

A dataframe including in the first column the variations performed, and in the following columns the corresponding Frobenius norms for the chosen model-preserving co-variations.

Details

Computation of the Frobenius norm between a Bayesian network and its updated version after a model-preserving variation.

References

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

Examples

Fro(synthetic_ci,"total",c(1,1),seq(0.9,1.1,0.01))
#>    Variation Frobenius
#> 1       0.90 -4.605170
#> 2       0.91 -4.815891
#> 3       0.92 -5.051457
#> 4       0.93 -5.318520
#> 5       0.94 -5.626821
#> 6       0.95 -5.991465
#> 7       0.96 -6.437752
#> 8       0.97 -7.013116
#> 9       0.98 -7.824046
#> 10      0.99 -9.210340
#> 11      1.00      -Inf
#> 12      1.01 -9.210340
#> 13      1.02 -7.824046
#> 14      1.03 -7.013116
#> 15      1.04 -6.437752
#> 16      1.05 -5.991465
#> 17      1.06 -5.626821
#> 18      1.07 -5.318520
#> 19      1.08 -5.051457
#> 20      1.09 -4.815891
#> 21      1.10 -4.605170
Fro(synthetic_ci,"partial",c(1,4),seq(0.9,1.1,0.01))
#>    Variation  Frobenius
#> 1       0.90         NA
#> 2       0.91 -0.2309237
#> 3       0.92 -0.4664898
#> 4       0.93 -0.7335526
#> 5       0.94 -1.0418540
#> 6       0.95 -1.4064971
#> 7       0.96 -1.8527842
#> 8       0.97 -2.4281483
#> 9       0.98 -3.2390785
#> 10      0.99 -4.6253729
#> 11      1.00       -Inf
#> 12      1.01 -4.6253729
#> 13      1.02 -3.2390785
#> 14      1.03 -2.4281483
#> 15      1.04 -1.8527842
#> 16      1.05         NA
#> 17      1.06         NA
#> 18      1.07         NA
#> 19      1.08         NA
#> 20      1.09         NA
#> 21      1.10         NA
Fro(synthetic_ci,"column",c(1,2),seq(0.9,1.1,0.01))
#>    Variation Frobenius
#> 1       0.90        NA
#> 2       0.91        NA
#> 3       0.92        NA
#> 4       0.93        NA
#> 5       0.94        NA
#> 6       0.95 -3.218876
#> 7       0.96 -3.665163
#> 8       0.97 -4.240527
#> 9       0.98 -5.051457
#> 10      0.99 -6.437752
#> 11      1.00      -Inf
#> 12      1.01 -6.437752
#> 13      1.02 -5.051457
#> 14      1.03 -4.240527
#> 15      1.04 -3.665163
#> 16      1.05 -3.218876
#> 17      1.06 -2.854233
#> 18      1.07 -2.545931
#> 19      1.08        NA
#> 20      1.09        NA
#> 21      1.10        NA
Fro(synthetic_ci,"row",c(3,2),seq(0.9,1.1,0.01))
#>    Variation  Frobenius
#> 1       0.90         NA
#> 2       0.91         NA
#> 3       0.92         NA
#> 4       0.93         NA
#> 5       0.94         NA
#> 6       0.95         NA
#> 7       0.96         NA
#> 8       0.97 -2.9526728
#> 9       0.98 -3.7636030
#> 10      0.99 -5.1498974
#> 11      1.00       -Inf
#> 12      1.01 -5.1498974
#> 13      1.02 -3.7636030
#> 14      1.03 -2.9526728
#> 15      1.04 -2.3773086
#> 16      1.05 -1.9310215
#> 17      1.06 -1.5663784
#> 18      1.07 -1.2580771
#> 19      1.08 -0.9910143
#> 20      1.09 -0.7554482
#> 21      1.10         NA

Frobenius norm for `CI`