SGL {SGL}

Fit a GLM with a Combination of Lasso and Group Lasso Regularization

Description

Fit a regularized generalized linear model via penalized maximum likelihood. The model is fit for a path of values of the penalty parameter. Fits linear, logistic and Cox models.

Usage

SGL(data, index, type = "linear", maxit = 1000, thresh = 0.001,
min.frac = 0.1, nlam = 20, gamma = 0.8, standardize = TRUE,
verbose = FALSE, step = 1, reset = 10, alpha = 0.95, lambdas = NULL)

Arguments

data

For type="linear" should be a list with $x$ an input matrix of dimension n-obs by p-vars, and $y$ a length $n$ response vector. For type="logit" should be a list with $x$, an input matrix, as before, and $y$ a length $n$ binary response vector. For type="cox" should be a list with x as before, time, an n-vector corresponding to failure/censor times, and status, an n-vector indicating failure (1) or censoring (0).

index

A p-vector indicating group membership of each covariate

type

model type: one of ("linear","logit", "cox")

maxit

Maximum number of iterations to convergence

thresh

Convergence threshold for change in beta

min.frac

The minimum value of the penalty parameter, as a fraction of the maximum value

nlam

Number of lambda to use in the regularization path

gamma

Fitting parameter used for tuning backtracking (between 0 and 1)

standardize

Logical flag for variable standardization prior to fitting the model.

verbose

Logical flag for whether or not step number will be output

step

Fitting parameter used for inital backtracking step size (between 0 and 1)

reset

Fitting parameter used for taking advantage of local strong convexity in nesterov momentum (number of iterations before momentum term is reset)

alpha

The mixing parameter. alpha = 1 is the lasso penalty. alpha = 0 is the group lasso penalty.

lambdas

A user specified sequence of lambda values for fitting. We recommend leaving this NULL and letting SGL self-select values

Details

The sequence of models along the regularization path is fit by accelerated generalized gradient descent.

Value

An object with S3 class "SGL"

beta

A p by nlam matrix, giving the penalized MLEs for the nlam different models, where the index corresponds to the penalty parameter lambda

lambdas

The actual sequence of lambda values used (penalty parameter)

type

Response type (linear/logic/cox)

intercept

For some model types, an intercept is fit

X.transform

A list used in predict which gives the empirical mean and variance of the x matrix used to build the model

lambdas

A user specified sequence of lambda values for fitting. We recommend leaving this NULL and letting SGL self-select values

Author(s)

Noah Simon, Jerry Friedman, Trevor Hastie, and Rob Tibshirani
Maintainer: Noah Simon [e-mail]

References

Simon, N., Friedman, J., Hastie, T., and Tibshirani, R. (2011) A Sparse-Group Lasso,
http://faculty.washington.edu/nrsimon/SGLpaper.pdf

See Also

cv.SGL

Examples

n = 50; p = 100; size.groups = 10
index <- ceiling(1:p / size.groups)
X = matrix(rnorm(n * p), ncol = p, nrow = n)
beta = (-2:2)
y = X[,1:5] %*% beta + 0.1*rnorm(n)
data = list(x = X, y = y)
fit = SGL(data, index, type = "linear")