Sparse group lasso regression (without cross-validation)

Fits an initial ridge regression to obtain weights for an adaptive lasso regression that allows for heterogeneous, overlapping and unknown groups of correlated variables.

Usage

corila(
  x,
  y,
  group,
  primary,
  family,
  hyper,
  alpha_init,
  alpha_final,
  cor,
  foldid,
  nfolds,
  lambda_init,
  threshold = 0
)

Arguments

x

\(n_0 \times p\) predictor matrix, where \(n_0\) is the number of observations used for model training and \(p\) is the number of variables

y

\(n_0\)-dimensional response vector, where \(n_0\) is the number of observations used for model training

group

group structure (three 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"

hyper

list of \(m\)-dimensional vectors or a data frame with \(m\) rows containing candidate values for the regularisation and mixing hyperparameters

alpha_init

elastic net mixing parameter (\(0 \leq\) alpha_init \(\leq 1\)) for initial regression (default: ridge penalisation with alpha_init=0); alternative choices are "pearson", "spearman", or "kendall" to use initial correlation coefficients (not implemented for family="cox"), "multiridge" for multi-penalty ridge regression with one penalty for each group (not implemented for family="poisson" or overlapping groups), or NA to set all initial coefficients equal to 1

alpha_final

elastic net mixing parameter for final regression (default: lasso penalisation with alpha_final=1)

cor

character string "pearson", "spearman" (default), or "kendall"; or \(p \times p\) correlation matrix

foldid

\(n_0\)-dimensional vector containing the fold identifiers

nfolds

integer specifying the number of folds

lambda_init

regularisation hyperparameter(s), or NULL (cross-validation)

threshold

threshold for absolute correlation coefficients: numeric in unit interval

Value

Returns an object of class "corila".

Details

The number of observations (samples) for training or testing are indicated by \(n_0\) and \(n_1\), respectively, the number of variables (features) is indicated by \(p\), and the number of variable groups is indicated by \(q\). Observations (samples) are indexed by \(i\) in \(\{1, \ldots, n\}\), variables (features) are indexed by \(j\) in \(\{1, \ldots, p\}\), and variable groups are indexed by \(k\) in \(\{1, \ldots, q\}\). The number of variables 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

Estimate parameters and tune hyperparameters (using cross-validation) with cv.corila(). Make predictions for a range of hyperparameters with predict().

This function calls .forescale() and .backscale() for standardising data and bringing results back to the original scale, respectively, .folds() for splitting samples into folds, .estim_initial_coefs() for obtaining initial coefficients, .is_adjacent() for identifying adjacent predictors, and glmnet::cv.glmnet() and glmnet::glmnet() for adaptive lasso regression.

Examples

# \donttest{
# simulation
n <- 100
p <- 50
group <- rep(x = 1:10, each = 5)
primary <- NULL
x <- matrix(data = rnorm(n * p), nrow = n, ncol = p)
y <- rnorm(n = n)

# model fitting
hyper <- data.frame(exp_local = 1, wgt_local = 0.5,
                    exp_global = 1, wgt_global = 0.5)
object <- corila(x = x,
                 y = y,
                 group = group,
                 primary = primary,
                 family = "gaussian",
                 alpha_init = 0,
                 alpha_final = 1,
                 cor = "spearman",
                 foldid = NULL,
                 nfolds = 10,
                 hyper = hyper,
                 lambda_init = NULL)
#> Error in corila(x = x, y = y, group = group, primary = primary, family = "gaussian",     alpha_init = 0, alpha_final = 1, cor = "spearman", foldid = NULL,     nfolds = 10, hyper = hyper, lambda_init = NULL): could not find function "corila"

y_hat <- stats::predict(object, newx = x, index = 1, s = 0)
#> Error: object 'object' not found
# }