RSAVS_Get_Lam_Max: Compute lam_max

In fenguoerbian/RSAVS: Robust Subgroup Analysis and Variable Selection

Compute lam_max

Description

This function computes the values of lam1_max or lam2_max which can shrink same type of covariates to the same value.

For beta, they will be shrinked to 0. For mu, the final value is determined by the type of loss function. Please refer to RSAVS_Get_Psi for more details. Basically, we have

\mu_0 = \mathrm{argmin}_{\mu} \sum_i\rho(y_i - \mu)

and

psi\_vec = (\psi(y_1 - \mu_0), \cdots, \psi(y_n - \mu_0))

where \psi = \partial \rho.

Usage

RSAVS_Get_Lam_Max(
  y_vec,
  x_mat,
  l_type = "L1",
  l_param = NULL,
  lam_ind = 1,
  const_abc = rep(1, 3),
  eps = 10^(-6)
)

Arguments

y_vec	numeric vector, the response
x_mat	numeric matrix, the covariate matrix
l_type	character string, type of loss function. "L1": l-1 loss(absolute value loss) "L2": l-2 loss(squared error loss) "Huber": Huber loss. Its parameter is given in l_param. Default value is "L1".
l_param	numeric vector containing necessary parameters of the corresponding loss function. The default value is NULL.
lam_ind	integer, indicating computation for mu or beta. 1: compute lam_max for mu. 2: compute lam_max for beta.
const_abc	a length-3 numeric vector, providing the scalars to adjust weight of regression function, penalty for subgroup identification and penalty for variable selection in the overall objective function. Defaults to c(1, 1, 1).
eps	a samll safe guard constant

Value

lam_max, a numerical variable

Note

For convex penalty like lasso, this lam_max can guarantee the global condition for shrinking the corresponding variables to the same value. For non-convex penalties such as SCAD and MCP, this is just a local condition.

See Also

RSAVS_Get_Psi.

fenguoerbian/RSAVS documentation built on Oct. 25, 2024, 3:16 p.m.