Sparse group lasso regression

Optimises the parameters and the hyperparameters of the sparse group lasso.

Usage

cv.corila(
  x,
  y,
  group,
  primary = NULL,
  family = "gaussian",
  alpha_init = 0,
  cor = "spearman",
  alpha_final = 1,
  nfolds = 10L,
  foldid = NULL,
  tune = "weight",
  na_action = "error",
  silent = FALSE
)

Arguments

x

\(n_0 \times p\) predictor matrix, containing only numerical values (continuous, integer, or binary), where \(n_0\) is the number of observations used for model training and \(p\) is the number of predictors

y

response vector of length \(n_0\), containing numerical values (family="gaussian"), integer values (family="poisson"), binary values (family="binomial"), or a survival object created with survival::Surv() (family="cox"), where \(n_0\) is the number of observations used for model training

group

group structure (multiple options):

• \(p\)-dimensional vector of group indices (in \(\{1, \ldots, q\}\)) or labels,

• list with \(q\) slots containing the variable indices (in \(\{1, \ldots, p\}\)) or labels,

• \(p \times p\) matrix, where the entry in the \(j^{\text{th}}\) row and the \(k^{\text{th}}\) column indicates whether information should be transferred from the \(j^{\text{th}}\) to the \(k^{\text{th}}\) variable

primary

\(p\)-dimensional logical vector indicating whether a predictor may be included in the final model (TRUE for "primary predictors") or must be excluded from the final model (FALSE for "auxiliary predictors")

family

character string "gaussian", "binomial", "poisson", or "cox"

alpha_init

A scalar specifying the method used for obtaining initial coefficients:

• a numeric scalar in the unit interval (\(0 \leq\) alpha_init \(\leq 1\)) to define the mixing parameter for elastic net regression (default: ridge penalisation with alpha_init=0);

• the character scalar "pearson", "spearman", or "kendall" to use initial correlation coefficients (not implemented for family="cox")

• the character scalar"multiridge" to use multi-penalty ridge regression with one penalty for each group (not implemented for family="poisson" or overlapping groups),

• NA to set all initial coefficients equal to 1

cor

character string "pearson", "spearman" (default), or "kendall"; or a correlation matrix (\(p\) rows, \(p\) columns, entries between \(-1\) and \(+1\))

alpha_final

elastic net mixing parameter for final regression: numeric between 0 for ridge penalisation and 1 for lasso penalisation (default: lasso penalisation with alpha_final=1)

nfolds

positive integer specifying the number of folds (minimum \(3\), maximum \(n\))

NB: If foldid is provided, nfolds is overwritten by max(foldid).

foldid

\(n_0\)-dimensional vector containing the fold identifiers (minimum \(1\), maximum nfolds)

tune

character string for determining the candidate values for the hyperparameters:

• "none": fixed weights and exponents (wgt_local=1, exp_local=1, wgt_global=0), no tuning

• "weight": fixed exponents (exp_local=0, exp_global=1), tuning wgt_local=1-wgt_global

• "exponent": fixed weights (wgt_local=1, wgt_global=0), tuning exp_local

• "bivariate": tuning wgt_local=1-wgt_global and exp_local=exp_global

• "factorial": tuning wgt_local, exp_local, wgt_global, exp_global

(to implement: data frame with columns wgt_local, exp_local, wgt_global, and exp_global)

na_action

character "error" to trigger an error if any observation has a missing predictor or a missing response or "complete_cases" to exclude observations with a missing predictor or a missing response from model fitting (while providing fitted values for these observations)

silent

Should messages from glmnet::glmnet() and glmnet::cv.glmnet() be suppressed? (logical scalar, FALSE or TRUE)

Value

Returns an object of class "cv.corila", a list with the following slots:

• model: list with one slot for each combination of hyperparameters, each slot contains an object of class "glmnet"

• hyper: data frame with one row for each combination of hyperparameters, four columns for the values of the hyperparameters (wgt_local, exp_local, wgt_global, and exp_global) and a column for the cross-validated loss (cvm)

• id_hyper: index of combination of hyperparameters leading to the lowest cross-validated loss

• lambda.min optimised regularisation hyperparameter

• scale: output from .forescale()

• y_hat: \(n\)-dimensional vector of fitted values

Details

The numbers of observations (samples) for training or testing are indicated by \(n_0\) and \(n_1\), respectively, the number of predictors (features) is indicated by \(p\), and the number of predictor group is indicated by \(q\). Observations are indexed by \(i\) in \(\{1, \ldots, n\}\), predictors are indexed by \(j\) in \(\{1, \ldots, p\}\), and predictor groups are indexed by \(k\) in \(\{1, \ldots, q\}\). The number of predictors in the \(k^{\text{th}}\) group is indicated by \(p_k\), with \(\sum_{k=1}^q p_k = p\) for non-overlapping groups.

References

Armin Rauschenberger (2026). "Sparse modelling with grouped and correlated features allowing for privileged information". In preparation.

See also

Extract coefficients with coef() and make predictions with predict().

This user function repeatedly calls corila() with different values for the regularisation and mixing hyperparameters.

The arguments of this function are validated with the helper functions listed here.

Examples

# \donttest{
data <- simulate_data()
model <- cv.corila(x = data$x_train,
                   y = data$y_train,
                   group = data$group,
                   primary = data$primary)
beta_hat <- coef(object = model)
y_hat <- predict(object = model, newx = data$x_test)
# }

# example for automatic mutation testing (with the R package autotest)
data <- simulate_data()
model <- cv.corila(x = data$x_train,
                   y = data$y_train,
                   group = as.double(data$group),
                   primary = data$primary,
                   alpha_init = 0.0,
                   foldid = rep(1:10, length.out = nrow(data$x_train)))