Penalty Derivative

Compute the derivative for a nonconvex penalty.

penalty_derivative(
  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

Value

A list of class penalty_derivative, including the following:

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

• lambda: Regularization parameter.

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 (Fan and Li 2001) . The default values in GGMncv are set to recommended values in the respective papers.

References

Fan J, Li R (2001). “Variable selection via nonconcave penalized likelihood and its oracle properties.” Journal of the American statistical Association, 96(456), 1348--1360.

Examples

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

head(deriv$deriv)
#>          deriv   thetas gamma penalty
#> 1 0.0002586469 5.000000  0.01    atan
#> 2 0.0002587504 4.999000  0.01    atan
#> 3 0.0002588539 4.998000  0.01    atan
#> 4 0.0002589576 4.997000  0.01    atan
#> 5 0.0002590612 4.996000  0.01    atan
#> 6 0.0002591650 4.994999  0.01    atan