Version: 1.0.0
Title: Stacked Elastic Net
Description: Implements stacked elastic net regression (Rauschenberger 2021 <doi:10.1093/bioinformatics/btaa535>). The elastic net generalises ridge and lasso regularisation (Zou 2005 <doi:10.1111/j.1467-9868.2005.00503.x>). Instead of fixing or tuning the mixing parameter alpha, we combine multiple alpha by stacked generalisation (Wolpert 1992 <doi:10.1016/S0893-6080(05)80023-1>).
Depends: R (≥ 3.0.0)
Imports: glmnet, survival, cornet, Matrix
Suggests: knitr, testthat, rmarkdown, CVXR, mvtnorm
License: GPL-3
Encoding: UTF-8
VignetteBuilder: knitr
RoxygenNote: 7.3.2
URL: https://github.com/rauschenberger/starnet/, https://rauschenberger.github.io/starnet/
BugReports: https://github.com/rauschenberger/starnet/issues
NeedsCompilation: no
Packaged: 2025-06-10 13:34:40 UTC; armin.rauschenberger
Author: Armin Rauschenberger ORCID iD [aut, cre]
Maintainer: Armin Rauschenberger <armin.rauschenberger@uni.lu>
Repository: CRAN
Date/Publication: 2025-06-10 14:00:02 UTC

Stacked Elastic Net Regression

Description

The R package starnet implements stacked elastic net regression. The elastic net generalises ridge and lasso regularisation. Instead of fixing or tuning the mixing parameter alpha, we combine multiple alphas by stacked generalisation.

Details

Use function starnet for model fitting. Type library(starnet) and then ?starnet or help("starnet)" to open its help file.

See the vignette for further examples. Type vignette("starnet") or browseVignettes("starnet") to open the vignette.

Author(s)

Maintainer: Armin Rauschenberger armin.rauschenberger@uni.lu (ORCID)

References

Armin Rauschenberger, Enrico Glaab, and Mark A. van de Wiel (2021). "Predictive and interpretable models via the stacked elastic net". Bioinformatics 37(14):2012-2016. doi:10.1093/bioinformatics/btaa535. (Click here to access PDF.)

See Also

Useful links:

glmnet::cv.glmnet

Description

Wrapper for cv.glmnet, with different handling of sparsity constraints.

Usage

.cv.glmnet(..., nzero)

Arguments

...

see cv.glmnet

nzero

maximum number of non-zero coefficients: positive integer

Value

Object of class cv.glmnet.

Examples

NA

Loss

Description

Calculate loss from predicted and observed values

Usage

.loss(y, x, family, type.measure, foldid = NULL, grouped = TRUE)

Arguments

y

observed values: numeric vector of length n

x

predicted values: numeric vector of length n

family

character "gaussian", "binomial", "poisson", "mgaussian", or "multinomial" (to implement: "cox")

type.measure

character "deviance", "mse", "mae", "class", or "auc"

foldid

fold identifiers: integer vector of length n, or NULL

grouped

logical (for "cox" only)

Examples

NA

Simulation

Description

Functions for simulating data

Usage

.simulate.block(n, p, mode, family = "gaussian")

Arguments

n

sample size: positive integer

p

dimensionality: positive integer

mode

character "sparse", "dense" or "mixed"

family

character "gaussian", "binomial" or "poisson"

Value

List of vector y and matrix X.

Examples

NA

Extract Coefficients

Description

Extracts pooled coefficients. (The meta learners weights the coefficients from the base learners.)

Usage

## S3 method for class 'starnet'
coef(object, nzero = NULL, ...)

Arguments

object

starnet object

nzero

maximum number of non-zero coefficients: positive integer, or NULL

...

further arguments (not applicable)

Value

List of scalar alpha and vector beta, containing the pooled intercept and the pooled slopes, respectively.

Examples



set.seed(1)
n <- 50; p <- 100
y <- rnorm(n=n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
object <- starnet(y=y,X=X)
coef <- coef(object)

Model comparison

Description

Compares stacked elastic net, tuned elastic net, ridge and lasso.

Usage

cv.starnet(
  y,
  X,
  family = "gaussian",
  nalpha = 21,
  alpha = NULL,
  nfolds.ext = 10,
  nfolds.int = 10,
  foldid.ext = NULL,
  foldid.int = NULL,
  type.measure = "deviance",
  alpha.meta = 1,
  nzero = NULL,
  intercept = NULL,
  upper.limit = NULL,
  unit.sum = NULL,
  ...
)

Arguments

y

response: numeric vector of length n

X

covariates: numeric matrix with n rows (samples) and p columns (variables)

family

character "gaussian", "binomial" or "poisson"

nalpha

number of alpha values

alpha

elastic net mixing parameters: vector of length nalpha with entries between 0 (ridge) and 1 (lasso); or NULL (equidistance)

nfolds.ext, nfolds.int, foldid.ext, foldid.int

number of folds (nfolds): positive integer; fold identifiers (foldid): vector of length n with entries between 1 and nfolds, or NULL, for hold-out (single split) instead of cross-validation (multiple splits): set foldid.ext to 0 for training and to 1 for testing samples

type.measure

loss function: character "deviance", "class", "mse" or "mae" (see cv.glmnet)

alpha.meta

meta-learner: value between 0 (ridge) and 1 (lasso) for elastic net regularisation; NA for convex combination

nzero

number of non-zero coefficients: scalar/vector including positive integer(s) or NA; or NULL (no post hoc feature selection)

intercept, upper.limit, unit.sum

settings for meta-learner: logical, or NULL (intercept=!is.na(alpha.meta), upper.limit=TRUE, unit.sum=is.na(alpha.meta))

...

further arguments (not applicable)

Value

List containing the cross-validated loss (or out-of sample loss if nfolds.ext equals two, and foldid.ext contains zeros and ones). The slot meta contains the loss from the stacked elastic net (stack), the tuned elastic net (tune), ridge, lasso, and the intercept-only model (none). The slot base contains the loss from the base learners. And the slot extra contains the loss from the restricted stacked elastic net (stack), lasso, and lasso-like elastic net (enet), with the maximum number of non-zero coefficients shown in the column name.

Examples



loss <- cv.starnet(y=y,X=X)

glmnet:::auc

Description

Import of auc (internal function)

Usage

glmnet.auc(y, prob, w)

Arguments

y

observed classes

prob

predicted probabilities

w

(ignored here)

Value

area under the ROC curve

Examples

NA

Makes Predictions

Description

Predicts outcome from features with stacked model.

Usage

## S3 method for class 'starnet'
predict(object, newx, type = "response", nzero = NULL, ...)

Arguments

object

starnet object

newx

covariates: numeric matrix with n rows (samples) and p columns (variables)

type

character "link" or "response"

nzero

maximum number of non-zero coefficients: positive integer, or NULL

...

further arguments (not applicable)

Value

Matrix of predicted values, with samples in the rows, and models in the columns. Included models are alpha (fixed elastic net), ridge (i.e. alpha0), lasso (i.e. alpha1), tune (tuned elastic net), stack (stacked elastic net), and none (intercept-only model).

Examples



set.seed(1)
n <- 50; p <- 100
y <- rnorm(n=n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
object <- starnet(y=y,X=X)
y_hat <- predict(object,newx=X[c(1),,drop=FALSE])

Print Values

Description

Prints object of class starnet.

Usage

## S3 method for class 'starnet'
print(x, ...)

Arguments

x

starnet object

...

further arguments (not applicable)

Value

Prints "stacked gaussian/binomial/poisson elastic net".

Examples



set.seed(1)
n <- 50; p <- 100
y <- rnorm(n=n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
object <- starnet(y=y,X=X)
print(object)

Stacked Elastic Net Regression

Description

Implements stacked elastic net regression.

Usage

starnet(
  y,
  X,
  family = "gaussian",
  nalpha = 21,
  alpha = NULL,
  nfolds = 10,
  foldid = NULL,
  type.measure = "deviance",
  alpha.meta = 1,
  penalty.factor = NULL,
  intercept = NULL,
  upper.limit = NULL,
  unit.sum = NULL,
  ...
)

Arguments

y

response: numeric vector of length n

X

covariates: numeric matrix with n rows (samples) and p columns (variables)

family

character "gaussian", "binomial" or "poisson"

nalpha

number of alpha values

alpha

elastic net mixing parameters: vector of length nalpha with entries between 0 (ridge) and 1 (lasso); or NULL (equidistance)

nfolds

number of folds

foldid

fold identifiers: vector of length n with entries between 1 and nfolds; or NULL (balance)

type.measure

loss function: character "deviance", "class", "mse" or "mae" (see cv.glmnet)

alpha.meta

meta-learner: value between 0 (ridge) and 1 (lasso) for elastic net regularisation; NA for convex combination

penalty.factor

differential shrinkage: vector of length n with entries between 0 (include) and Inf (exclude), or NULL (all 1)

intercept, upper.limit, unit.sum

settings for meta-learner: logical, or NULL (intercept=!is.na(alpha.meta), upper.limit=TRUE, unit.sum=is.na(alpha.meta))

...

further arguments passed to glmnet

Details

Post hoc feature selection: consider argument nzero in functions coef and predict.

Value

Object of class starnet. The slots base and meta contain cv.glmnet-like objects, for the base and meta learners, respectively.

References

Armin Rauschenberger, Enrico Glaab, and Mark A. van de Wiel (2021). "Predictive and interpretable models via the stacked elastic net". Bioinformatics 37(14):2012-2016. doi:10.1093/bioinformatics/btaa535. (Click here to access PDF.)

Examples



set.seed(1)
n <- 50; p <- 100
y <- rnorm(n=n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
object <- starnet(y=y,X=X,family="gaussian")

Extract Weights

Description

Extracts coefficients from the meta learner, i.e. the weights for the base learners.

Usage

## S3 method for class 'starnet'
weights(object, ...)

Arguments

object

starnet object

...

further arguments (not applicable)

Value

Vector containing intercept and slopes from the meta learner.

Examples



set.seed(1)
n <- 50; p <- 100
y <- rnorm(n=n)
X <- matrix(rnorm(n*p),nrow=n,ncol=p)
object <- starnet(y=y,X=X)
weights(object)