Maximum information preservable by supervised nominal lumping

Calculates the maximum amount of mutual information between a lumped nominal covariate and a discrete outcome that can be preserved by lumping.

Usage

maximum_mutual_information_nominal_supervised(
  joint_counts,
  threshold,
  adj_matrix = NULL,
  verbose = FALSE
)

Arguments

joint_counts

Named numeric matrix with one row per level and one column per outcome category. Row names must identify the levels. Entry (k, y) is the number of observations with covariate level k and outcome y.

threshold

Minimum number of samples each lumped level must contain.

adj_matrix

Adjacency matrix of the preference graph. Default: a complete graph, allowing all lumpings.

verbose

Whether to print diagnostic messages. Default: FALSE.

Value

A list containing information about the optimal lumping:

mutual_information

Mutual information between the lumped covariate and the outcome, in nats.

loss

Mutual information lost by the lumping.

lumping

A list of character vectors, where each vector contains the names of the original levels that have been lumped together.

Details

Be advised that, since the problem is NP-hard, the implementation here has time complexity \(O\left(2^{2^m}\right)\), where \(m\) is the number of levels in the nominal variable.

See also

maximum_mutual_information_nominal() for the unsupervised version.

maximum_mutual_information_hierarchical_supervised() for a version that exploits hierarchical structure to speed up execution.

maximum_mutual_information_nominal_supervised_continuous() for a version that accepts a continuous outcome.

Author

Daan Koning

Examples

joint_counts <- matrix(
  c(8, 2, 1, 4, 1, 2),
  nrow = 3,
  dimnames = list(c("A", "B", "C"), c("y0", "y1"))
)
maximum_mutual_information_nominal_supervised(joint_counts, threshold = 3)
#> $mutual_information
#> [1] 0.03173431
#> 
#> $loss
#> [1] -2.220446e-16
#> 
#> $lumping
#> $lumping[[1]]
#> [1] "C"
#> 
#> $lumping[[2]]
#> [1] "B"
#> 
#> $lumping[[3]]
#> [1] "A"
#> 
#>