as_sgs {sgs}

fits the adaptively scaled SGS model (AS-SGS)

Description

Fits an SGS model using the noise estimation procedure, termed adaptively scaled SGS (Algorithm 2 from Feser et al (2023)). This adaptively estimates \lambda and then fits the model using the estimated value. It is an alternative approach to cross-validation (fit_sgs_cv()). The approach is only compatible with the SGS penalties.

Usage

as_sgs(
  X,
  y,
  groups,
  type = "linear",
  pen_method = 2,
  alpha = 0.95,
  vFDR = 0.1,
  gFDR = 0.1,
  standardise = "l2",
  intercept = TRUE,
  verbose = FALSE
)

Arguments

X

Input matrix of dimensions n \times p. Can be a sparse matrix (using class "sparseMatrix" from the Matrix package).

y

Output vector of dimension n. For type="linear" should be continuous and for type="logistic" should be a binary variable.

groups

A grouping structure for the input data. Should take the form of a vector of group indices.

type

The type of regression to perform. Supported values are: "linear" and "logistic".

pen_method

The type of penalty sequences to use.

• "1" uses the vMean and gMean SGS sequences.

• "2" uses the vMax and gMax SGS sequences.

alpha

The value of \alpha, which defines the convex balance between SLOPE and gSLOPE. Must be between 0 and 1.

vFDR

Defines the desired variable false discovery rate (FDR) level, which determines the shape of the variable penalties. Must be between 0 and 1.

gFDR

Defines the desired group false discovery rate (FDR) level, which determines the shape of the group penalties. Must be between 0 and 1.

standardise

Type of standardisation to perform on X:

• "l2" standardises the input data to have \ell_2 norms of one.

• "l1" standardises the input data to have \ell_1 norms of one.

• "sd" standardises the input data to have standard deviation of one.

• "none" no standardisation applied.

intercept

Logical flag for whether to fit an intercept.

verbose

Logical flag for whether to print fitting information.

Value

An object of type "sgs" containing model fit information (see fit_sgs()).

References

F. Feser, M. Evangelou Sparse-group SLOPE: adaptive bi-level selection with FDR-control, https://arxiv.org/abs/2305.09467