regularizationWeights: Generate Regularization (Penalty) Weights for SLOPE

Description

This function generates sequences of regularizations weights for use in SLOPE() (or elsewhere).

Usage

regularizationWeights(
  n_lambda = 100,
  type = c("bh", "gaussian", "oscar", "lasso"),
  q = 0.2,
  theta1 = 1,
  theta2 = 0.5,
  n = NULL
)

Value

A vector of length n_lambda with regularization weights.

Arguments

n_lambda: The number of lambdas to generate. This should typically be equal to the number of predictors in your data set.
type: The type of lambda sequence to use. See documentation for in SLOPE(), including that related to the lambda parameter in that function.
q: parameter controlling the shape of the lambda sequence, with usage varying depending on the type of path used and has no effect is a custom lambda sequence is used. Must be greater than 1e-6 and smaller than 1.
theta1: parameter controlling the shape of the lambda sequence when lambda == "OSCAR". This parameter basically sets the intercept for the lambda sequence and is equivalent to \(\lambda_1\) in the original OSCAR formulation.
theta2: parameter controlling the shape of the lambda sequence when lambda == "OSCAR". This parameter basically sets the slope for the lambda sequence and is equivalent to \(\lambda_2\) in the original OSCAR formulation.
n: The number of rows (observations) in the design matrix.

Details

Please see SLOPE() for detailed information regarding the parameters in this function, in particular the section Regularization Sequences.

Note that these sequences are automatically scaled (unless a value for the alpha parameter is manually supplied) when using SLOPE(). In this function, nu such scaling is attempted.

Examples

Run this code

# compute different penalization sequences
bh <- regularizationWeights(100, q = 0.2, type = "bh")

gaussian <- regularizationWeights(
  100,
  q = 0.2,
  n = 300,
  type = "gaussian"
)

oscar <- regularizationWeights(
  100,
  theta1 = 1.284,
  theta2 = 0.0182,
  type = "oscar"
)

lasso <- regularizationWeights(100, type = "lasso") * mean(oscar)

# Plot a comparison between these sequences
plot(bh, type = "l", ylab = expression(lambda))
lines(gaussian, col = "dark orange")
lines(oscar, col = "navy")
lines(lasso, col = "red3")

legend(
  "topright",
  legend = c("BH", "Gaussian", "OSCAR", "lasso"),
  col = c("black", "dark orange", "navy", "red3"),
  lty = 1
)