penalty_function function

Penalty Function

Compute the penalty function for nonconvex penalties.

penalty_function(
  theta = seq(-5, 5, length.out = 1e+05),
  penalty = "atan",
  lambda = 1,
  gamma = c(0.01, 0.05)
)

Arguments

• theta: Numeric vector. Values for which the derivative is computed.
• penalty: Character string. Which penalty should be used (defaults to "atan")? See ggmncv for the available penalties.
• lambda: Numeric. Regularization parameter (defaults to 1).
• gamma: Numeric vector. Hyperparameter(s) for the penalty function

Returns

A list of class penalty_function, including the following:

• deriv: Data frame including the penalty function, theta, gamma, and the chosen penalty.

Note

Some care is required for specifying gamma. For example, the default value for scad is 3.7 and it must be some value greater than 2 if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_citeOnly(keys="fan2001variable",package="GGMncv",cached_env=.Rdpack.currefs) . The default values in GGMncv are set to recommended values in the respective papers.

Examples

func <- penalty_function(theta =  seq(-5,5,length.out = 10000),
                            lambda = 1,
                            gamma = c(0.01, 0.05, 0.1))

head(func$pen)

References

if(!exists(".Rdpack.currefs")) .Rdpack.currefs <-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)