Maximum information preservable by supervised continuous nominal lumping

Calculates the maximum Ross-estimated mutual information between a lumped nominal covariate and a numeric outcome.

Usage

maximum_mutual_information_nominal_supervised_continuous(
  x,
  y,
  threshold,
  adj_matrix = NULL,
  verbose = FALSE,
  k = 3L
)

Arguments

x

Nominal covariate. A factor is used in factor level order; otherwise the sorted unique values define the level order.

y

Numeric outcome vector.

threshold

Minimum number of samples each lumped level must contain.

adj_matrix

Adjacency matrix of the preference graph. Default: complete graph, allowing all admissible cliques.

verbose

Whether to print diagnostic messages. Default: FALSE.

k

Number of nearest neighbours used by the Ross estimator. Default: 3.

Value

A list containing information about the optimal lumping:

mutual_information

Ross-estimated 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.

See also

maximum_mutual_information_nominal_supervised() for the discrete-outcome version.

maximum_mutual_information_ordinal_supervised_continuous() for the ordinal analogue.

lump_nominal_supervised() for a user-friendly wrapper that applies the lumping.

Author

Daan Koning

Examples

set.seed(1)
x <- factor(rep(c("A", "B", "C"), each = 5))
y <- c(rnorm(5, 0), rnorm(5, 0), rnorm(5, 3))
maximum_mutual_information_nominal_supervised_continuous(x, y, threshold = 5)
#> $mutual_information
#> [1] 0.2151883
#> 
#> $loss
#> [1] 4.440892e-16
#> 
#> $lumping
#> $lumping[[1]]
#> [1] "C"
#> 
#> $lumping[[2]]
#> [1] "B"
#> 
#> $lumping[[3]]
#> [1] "A"
#> 
#>