fit_sgs_cv {sgs}

Fit an SGS model using k-fold cross-validation.

Description

Function to fit a pathwise solution of sparse-group SLOPE (SGS) models using k-fold cross-validation. Supports both linear and logistic regression, both with dense and sparse matrix implementations.

Usage

fit_sgs_cv(
  X,
  y,
  groups,
  type = "linear",
  lambda = "path",
  path_length = 20,
  min_frac = 0.05,
  alpha = 0.95,
  vFDR = 0.1,
  gFDR = 0.1,
  pen_method = 1,
  nfolds = 10,
  backtracking = 0.7,
  max_iter = 5000,
  max_iter_backtracking = 100,
  tol = 1e-05,
  standardise = "l2",
  intercept = TRUE,
  error_criteria = "mse",
  screen = TRUE,
  verbose = FALSE,
  v_weights = NULL,
  w_weights = NULL
)

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".

lambda

The regularisation parameter. Defines the level of sparsity in the model. A higher value leads to sparser models:

• "path" computes a path of regularisation parameters of length "path_length". The path will begin just above the value at which the first predictor enters the model and will terminate at the value determined by "min_frac".

• User-specified single value or sequence. Internal scaling is applied based on the type of standardisation. The returned "lambda" value will be the original unscaled value(s).

path_length

The number of \lambda values to fit the model for. If "lambda" is user-specified, this is ignored.

min_frac

Defines the termination point of the pathwise solution, so that \lambda_\text{min} = min_frac \cdot \lambda_\text{max}.

alpha

The value of \alpha, which defines the convex balance between SLOPE and gSLOPE. Must be between 0 and 1. Recommended value is 0.95.

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.

pen_method

The type of penalty sequences to use (see Feser and Evangelou (2023)):

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

• "2" uses the vMax SGS and gMean gSLOPE sequences.

• "3" uses the BH SLOPE and gMean gSLOPE sequences, also known as SGS Original.

nfolds

The number of folds to use in cross-validation.

backtracking

The backtracking parameter, \tau, as defined in Pedregosa et. al. (2018).

max_iter

Maximum number of ATOS iterations to perform.

max_iter_backtracking

Maximum number of backtracking line search iterations to perform per global iteration.

tol

Convergence tolerance for the stopping criteria.

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.

error_criteria

The criteria used to discriminate between models along the path. Supported values are: "mse" (mean squared error) and "mae" (mean absolute error).

screen

Logical flag for whether to apply screening rules (see Feser and Evangelou (2024)). Screening discards irrelevant groups before fitting, greatly improving speed.

verbose

Logical flag for whether to print fitting information.

v_weights

Optional vector for the variable penalty weights. Overrides the penalties from pen_method if specified. When entering custom weights, these are multiplied internally by \lambda and \alpha. To void this behaviour, set \lambda = 2 and \alpha = 0.5

w_weights

Optional vector for the group penalty weights. Overrides the penalties from pen_method if specified. When entering custom weights, these are multiplied internally by \lambda and 1-\alpha. To void this behaviour, set \lambda = 2 and \alpha = 0.5

Details

Fits SGS models under a pathwise solution using adaptive three operator splitting (ATOS), picking the 1se model as optimum. Warm starts are implemented.

Value

A list containing:

all_models

A list of all the models fitted along the path.

fit

The 1se chosen model, which is a "sgs" object type.

best_lambda

The value of \lambda which generated the chosen model.

best_lambda_id

The path index for the chosen model.

errors

A table containing fitting information about the models on the path.

type

Indicates which type of regression was performed.

References

Feser, F., Evangelou, M. (2023). Sparse-group SLOPE: adaptive bi-level selection with FDR-control, https://arxiv.org/abs/2305.09467

Feser, F., Evangelou, M. (2024). Strong screening rules for group-based SLOPE models, https://arxiv.org/abs/2405.15357

See Also

fit_sgs()

Other model-selection: as_sgs(), fit_gslope_cv(), scaled_sgs()

Other SGS-methods: as_sgs(), coef.sgs(), fit_sgs(), plot.sgs(), predict.sgs(), print.sgs(), scaled_sgs()

Examples

# specify a grouping structure
groups = c(1,1,1,2,2,3,3,3,4,4)
# generate data
data =  gen_toy_data(p=10, n=5, groups = groups, seed_id=3,group_sparsity=1)
# run SGS with cross-validation (the proximal functions can be found in utils.R)
cv_model = fit_sgs_cv(X = data$X, y = data$y, groups=groups, type = "linear", 
path_length = 5, nfolds=5, alpha = 0.95, vFDR = 0.1, gFDR = 0.1, min_frac = 0.05, 
standardise="l2",intercept=TRUE,verbose=TRUE)