argminCS (version 1.1.0)

lambda.adaptive.LOO: Generate a scaled.difference.matrix-driven \(\lambda\) for LOO algorithm.

Description

Generate a scaled.difference.matrix-driven \(\lambda\) for LOO algorithm motivated by the derivation of the first order stability. For its precise definition, we refer to the paper Zhang et al 2024.

Usage

lambda.adaptive.LOO(
  scaled.difference.matrix,
  sample.mean = NULL,
  const = 2.5,
  seed = NULL
)

Value

A scaled.difference.matrix-driven \(\lambda\) for LOO algorithm.

Arguments

scaled.difference.matrix

A n by (p-1) difference scaled.difference.matrix matrix after column-wise scaling (reference dimension - the rest); each of its row is a (p-1)-dimensional vector of differences.

sample.mean

The sample mean of the n samples in scaled.difference.matrix; defaults to NULL. It can be calculated via colMeans(scaled.difference.matrix).

const

A scaling constant for the scaled.difference.matrix driven \(\lambda\); defaults to 2.5. As its value gets larger, the first order stability tends to increase while power might decrease.

seed

(Optional) If provided, used to seed for tie-breaking (for reproducibility).

Examples

# Simulate data
set.seed(123)
r <- 4
n <- 200
mu <- (1:20)/20
cov <- diag(length(mu))
set.seed(108)
data <- MASS::mvrnorm(n, mu, cov)
sample.mean <- colMeans(data)
diff.mat <- get.difference.matrix(data, r)
sample.mean.r <- get.sample.mean.r(sample.mean, r)
lambda <- lambda.adaptive.LOO(diff.mat, sample.mean=sample.mean.r)