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Composite Pairwise Loss Function

Source: R/alf.R
composite_pair_loss.Rd

Computes the total loss across all pairwise combinations of rows in a matrix.

Usage

composite_pair_loss(x, fun, trans = identity, rescale = "df", ...)

Arguments

x

A numeric vector, matrix, or data frame. If not a matrix, it will be coerced to one after applying the transformation function.

fun

A function to compute the loss for each pairwise difference. The package supports the alignment loss (alf) and the approximate L0 penalty (l0a), but users can provide custom functions as well.

trans

A transformation function to apply to x before computing pairwise differences. Default is identity (no transformation).

rescale

Either "df" (default) to rescale the total loss by (nrow - 1) / ncombn(nrow, 2), where nrow is the number of rows, or a numeric value (likely between 0 and 1) to multiply the total loss by. With rescale = "df" and a 0/1-valued fun such as l0a, the returned value approximates the number of degrees of freedom of non-invariance in the block: 0 when all rows are equal (full invariance) and nrow - 1 per column when all rows differ (fully free). It soft-counts how many of the nrow - 1 pairwise-invariance constraints per column are violated.

...

Additional arguments passed to the loss function fun.

Value

A numeric scalar representing the sum of losses across all pairwise combinations of rows.

Details

The function works by:

  1. Applying the transformation function trans to the input x

  2. Converting the result to a matrix

  3. Generating all possible pairwise combinations of row indices

  4. Computing the difference between each pair of rows

  5. Applying the loss function fun to each difference

  6. Summing all the individual losses

effective_df() builds on this degrees-of-freedom interpretation (rescale = "df" with a 0/1-valued fun such as l0a) to report the effective number of parameters, and hence the effective model degrees of freedom, of penalized fits returned by penalized_est().

Examples

# Example with a simple matrix
x <- matrix(runif(12), nrow = 4)
composite_pair_loss(x, fun = alf)
#> [1] 5.075207

# Example with log transformation and L2 loss
composite_pair_loss(x, fun = function(x) x^2, trans = log)
#> [1] 35.18578