Package 'sparselink'

Sparse regression for related problems

Description

The R package 'sparselink' implements sparse regression for related problems (multi-task learning and transfer learning).

Details

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

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

Author(s)

Maintainer: Armin Rauschenberger [email protected] (ORCID)

References

Armin Rauschenberger, Petr N. Nazarov, and Enrico Glaab (2025). "Estimating sparse regression models in multi-task learning and transfer learning through adaptive penalisation". Under revision. https://hdl.handle.net/10993/63425

See Also

First use sparselink to fit the models, and then coef to extract coefficients or predict to make predictions.

Examples

?sparselink
?coef.sparselink
?predict.sparselink

---

Regression Coefficients

Description

Extracts coefficients from multi-task or transfer learning regression model.

Usage

## S3 method for class 'sparselink'
coef(object, ...)

Arguments

object	object of class "sparselink" (generated by function sparselink)
...	(not applicable)

Value

Returns estimated coefficients. The output is a list with two slots: slot alpha with the estimated intercept (vector of length $q$), and slot beta with the estimated slopes (matrix with $p$ rows and $q$ columns).

References

Armin Rauschenberger, Petr N. Nazarov, and Enrico Glaab (2025). "Estimating sparse regression models in multi-task learning and transfer learning through adaptive penalisation". Under revision. https://hdl.handle.net/10993/63425

See Also

Use sparselink to fit the model and predict to make predictions.

Examples

family <- "gaussian"
type <- "multiple" #  try "multiple" or "transfer"
if(type=="multiple"){
 data <- sim_data_multi(family=family)
} else if(type=="transfer"){
 data <- sim_data_trans(family=family)
}

object <- sparselink(x=data$X_train,y=data$y_train,family=family)
coef <- coef(object=object)

---

Out-of-sample Predictions

Description

Predicts outcomes with a multi-task or transfer learning regression model.

Usage

## S3 method for class 'sparselink'
predict(object, newx, weight = NULL, ...)

Arguments

object	object of class "sparselink" (generated by function sparselink)
newx	features: matrix with $n$ rows (samples) and $p$ columns (variables) for multi-task learning; list of $q$ matrices with $n_k$ rows (samples) and $p$ columns (variables) for transfer learning, for each $k$ in $1,\ldots,q$
weight	hyperparameters for scaling external and internal weights: numeric vector of length 2, with the first entry for the external weights (prior coefficients from source data), and the second entry for the internal weights (prior coefficients from target data), selected values must be among the candidate values, default: NULL (using cross-validated weights)
...	(not applicable)

Value

Returns predicted values or predicted probabilities. The output is a list of $q$ column vectors of length $n_k$ for $k$ in $1,\ldots,q$. Each vector corresponds to one target (multi-task learning) or one dataset (transfer learning).

References

Armin Rauschenberger, Petr N. Nazarov, and Enrico Glaab (2025). "Estimating sparse regression models in multi-task learning and transfer learning through adaptive penalisation". Under revision. https://hdl.handle.net/10993/63425

See Also

Use sparselink to fit the model and coef to extract coefficients.

Examples

family <- "gaussian"
type <- "multiple" # try "multiple" or "transfer"
if(type=="multiple"){
 data <- sim_data_multi(family=family)
} else if(type=="transfer"){
 data <- sim_data_trans(family=family)
}

object <- sparselink(x=data$X_train,y=data$y_train,family=family)
y_hat <- predict(object=object,newx=data$X_test)

---

Sparse regression for related problems

Description

Estimates sparse regression models (i.e., performing feature selection) in multi-task learning or transfer learning. Multi-task learning involves multiple targets, and transfer learning involves multiple datasets.

Usage

sparselink(
  x,
  y,
  family,
  alpha.init = 0.95,
  alpha = 1,
  type = "exp",
  nfolds = 10,
  cands = NULL
)

Arguments

x	$n \times p$ matrix (multi-task learning) or list of $n_k \times p$ matrices (transfer learning)
y	$n \times q$ matrix (multi-task learning) or list of $n_k$-dimensional vectors (transfer learning)
family	character "gaussian" or "binomial"
alpha.init	elastic net mixing parameter for initial regressions, default: 0.95 (lasso-like elastic net)
alpha	elastic net mixing parameter of final regressions, default: 1 (lasso)
type	default "exp" scales weights with $w_{ext}^{v_{ext}}+w_{int}^{v_{int}}$ (see internal function construct_penfacs for details)
nfolds	number of internal cross-validation folds, default: 10 (10-fold cross-validation)
cands	candidate values for both scaling parameters, default: NULL ({0, 0.2, 0.4, 0.6, 0.8, 1})

Value

Returns an object of class sparselink, a list with multiple slots:

• Stage 1 regressions (before sharing information): Slot glm.one contains $q$ objects of type cv.glmnet (one for each problem).

• Candidate scaling parameters (exponents): Slot weight contains a data frame with $n$ combinations of exponents for the external (source) and internal (target) weights

• Stage 2 regressions (after sharing information): Slot glm.two contains $q$ lists (one for each problem) of $n$ objects of type cv.glmnet (one for each combination of exponents).

• Optimal regularisation parameters: Slot lambda.min contains the cross-validated regularisation parameters for the stage 2 regressions.

• Optimal scaling parameters: Slots weight.ind and weight.min indicate or contain the cross-validated scaling parameters.

References

Armin Rauschenberger, Petr N. Nazarov, and Enrico Glaab (2025). "Estimating sparse regression models in multi-task learning and transfer learning through adaptive penalisation". Under revision. https://hdl.handle.net/10993/63425

See Also

Use coef to extract coefficients and predict to make predictions.

Examples

#--- multi-task learning ---
n <- 100
p <- 200
q <- 3

family <- "gaussian"
x <- matrix(data=rnorm(n=n*p),nrow=n,ncol=p)
y <- matrix(data=rnorm(n*q),nrow=n,ncol=q)
object <- sparselink(x=x,y=y,family=family)

#--- transfer learning ---
n <- c(100,50)
p <- 200

x <- lapply(X=n,function(x) matrix(data=stats::rnorm(n*p),nrow=x,ncol=p))
y <- lapply(X=n,function(x) stats::rnorm(x))
family <- "gaussian"
object <- sparselink(x=x,y=y,family=family)

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