Package {sglssnal}

Extract estimated coefficients from a sglssnal object

Description

Extract estimated coefficients from a sglssnal object

Usage

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

Arguments

Value

A numeric matrix of estimated coefficients.

Examples

set.seed(1)
n <- 50
p <- 20
A <- matrix(rnorm(n * p), n, p)
b <- rnorm(n)
group <- rep(1:4, each = 5)

fit <- sglssnal(A, b, group, lambda = 0.5, alpha = 0.5)
coef(fit)

Cross-validation for sglssnal

Description

Perform cross-validation for the sglssnal algorithm over a path of lambda values.

Usage

cv.sglssnal(
  A,
  b,
  group,
  alpha = 0.05,
  lambda = NULL,
  nlambda = 100,
  lambda_min_ratio = 1e-04,
  nfolds = 5,
  foldid = NULL,
  verbose = 1L,
  stoptol = 1e-06,
  stoptolcv = 1e-04,
  ...
)

Arguments

Value

List of class ⁠cv.sglssnal, sglssnal⁠, containing the following components:

• obj: Matrix containing primal and dual objective values for the solution.

• x: Matrix of primal variables, with each column corresponding to a lambda.

• x0: Vector of intercept values for each lambda.

• y: Matrix of y dual variables, with each column corresponding to a lambda.

• z: Matrix of z dual variables, with each column corresponding to a lambda.

• info: List containing information about the optimization process.

• cv_info: List containing the lambdas, cross-validation errors, and the index of the optimal lambda.

Examples

set.seed(1)
n <- 50
p <- 20
A <- matrix(rnorm(n * p), n, p)
bstar <- c(rnorm(5), rep(0, p - 5))
b <- as.numeric(A %*% bstar + rnorm(n, sd = 0.1))
group <- rep(1:4, each = 5)

cvfit <- cv.sglssnal(A, b, group, nlambda = 10, nfolds = 3)
cvfit$cv_info$cv_lambda_id

Predict method for sglssnal objects

Description

Predict method for sglssnal objects

Usage

## S3 method for class 'sglssnal'
predict(object, newdata, ...)

Arguments

Value

A numeric matrix of predictions, with columns corresponding to lambda values.

Examples

set.seed(1)
n <- 50
p <- 20
A <- matrix(rnorm(n * p), n, p)
b <- rnorm(n)
group <- rep(1:4, each = 5)

fit <- sglssnal(A, b, group, lambda = 0.5, alpha = 0.5)
predict(fit, A)

Riboflavin production and gene expression, grouped by GO Slim term

Description

A real, pre-processed dataset of riboflavin (vitamin B2) production by engineered Bacillus subtilis strains, arranged for direct use with sglssnal()/cv.sglssnal(). Predictors are gene expression levels; genes are grouped by their "generic GO Slim" Biological Process term (36 groups).

Usage

riboflavin

Format

A list with components:

A

71 x 1199 numeric matrix of log gene-expression levels, one row per strain variant, one column per gene. Column names are the original Affymetrix probe IDs (e.g. "AADK_at"); row names are the original microarray scan identifiers.

b

Length-71 numeric vector of log-transformed riboflavin production rate.

group

Length-1199 character vector giving the GO term ID (e.g. "GO:0006766") for each column of A, suitable for the group argument of sglssnal(). Group sizes range from 284 genes (transmembrane transport) down to singletons. 13% of these genes have GO annotations spanning more than one Slim term; since group requires a strict partition, each such gene was assigned to its most-frequently annotated Slim term.

Source

Gene expression and production-rate data: Bühlmann, P., Kalisch, M. and Meier, L. (2014). High-dimensional statistics with a view towards applications in biology. Annual Review of Statistics and its Application, 1, 255-278. Data kindly provided by DSM (Switzerland); originally distributed in the hdi package. Gene-to-GO-term annotations: UniProt-GOA B. subtilis 168 proteome annotation file, https://ftp.ebi.ac.uk/pub/databases/GO/goa/proteomes/ (GO release 2026-07-26). GO Slim term set: goslim_generic, https://current.geneontology.org/ontology/subsets/goslim_generic.obo. Gene Ontology Consortium data and data products are licensed under CC BY 4.0; see https://geneontology.org/docs/go-citation-policy/.

Examples

fit <- sglssnal(riboflavin$A, riboflavin$b, riboflavin$group, lambda = 0.05)
coef(fit)

Run Sparse-Group Lasso via Semismooth Newton Augmented Lagrangian

Description

Fits a sparse-group lasso model using second-order information to solve the dual problem. The penalty function is given by

\Phi(x) = \alpha\lambda ||x||_1 + (1-\alpha)\lambda \sum_{i=1}^g w_i ||x_{G_i}||_2

where G_i is the i-th group, w_i its penalty factor, and \alpha \in [0, 1] mixes the \ell_1 and group \ell_2 penalties. The primal problem is given by

\min_{x \in \mathbb{R}^p}\; \frac{1}{2} ||Ax - b||_2^2 + \Phi(x)

while the dual problem has the form

\begin{matrix} \max_{y \in \mathbb{R}^n, z \in \mathbb{R}^p}\; -\langle b, y\rangle - \frac{1}{2}||y||_2^2 - \Phi^\ast(z) \\ \text{s.t.}\; A^\top y + z = 0 \end{matrix}

where \Phi^\ast(z) denotes the Fenchel conjugate of \Phi. The algorithm is based on the work of Zhang et al. (2020).

Usage

sglssnal(
  A,
  b,
  group,
  lambda = NULL,
  nlambda = 100,
  lambda_min_ratio = 1e-04,
  alpha = 0.05,
  pfgroup = sqrt(as.numeric(table(group))),
  intercept = TRUE,
  standardize = TRUE,
  stoptol = 1e-06,
  stopopt = 2L,
  verbose = 1L,
  maxit = 5000L,
  Lip = NULL,
  y0 = NULL,
  z0 = NULL,
  x0 = NULL
)

Arguments

Value

List of class sglssnal containing the following components:

• obj: Matrix containing primal and dual objective values for each lambda.

• x: Matrix of primal variables, with each column corresponding to a lambda.

• x0: Vector of intercept values for each lambda.

• y: Matrix of y dual variables, with each column corresponding to a lambda.

• z: Matrix of z dual variables, with each column corresponding to a lambda.

• info: List containing information about the optimization process for each lambda.

• lambda: Vector of lambda values used.

References

Zhang, Y., Zhang, N., Sun, D., & Toh, K. C. (2020). An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems. Mathematical Programming, 179, 223-263. doi:10.1007/s10107-018-1329-6.

Examples

set.seed(1)
n <- 50
p <- 20
A <- matrix(rnorm(n * p), n, p)
bstar <- c(rnorm(5), rep(0, p - 5))
b <- as.numeric(A %*% bstar + rnorm(n, sd = 0.1))
group <- rep(1:4, each = 5)

fit <- sglssnal(A, b, group, lambda = 0.5, alpha = 0.5)
coef(fit)