Overlapping Group Lasso (OGLasso)

oglasso(
  x,
  y,
  delta = NULL,
  group,
  fused = NULL,
  family = c("gaussian", "binomial", "coxph"),
  nlambda = 100L,
  lambda = NULL,
  lambda.min.ratio = NULL,
  lambda.fused = 0,
  alpha = NULL,
  group.weights = NULL,
  adaptive.lasso = FALSE,
  adaptive.fused = FALSE,
  penalty.factor = NULL,
  penalty.factor.fused = NULL,
  gamma = 1,
  standardize = TRUE,
  intercept = TRUE,
  compute.se = FALSE,
  rho = NULL,
  dynamic.rho = TRUE,
  maxit = 500L,
  abs.tol = 1e-05,
  rel.tol = 1e-05,
  irls.tol = 1e-05,
  irls.maxit = 100L
)

Arguments

x	input matrix of dimension nobs by nvars. Each row is an observation, each column corresponds to a covariate
y	numeric response vector of length nobs
delta	vector of length equal to the number of observations with values in 1 and 0, where a 1 indicates the observed time is a death and a 0 indicates the observed time is a censoring event
group	A list of length equal to the number of groups containing vectors of integers indicating the variable IDs for each group. For example, `group = list(c(1,2), c(2,3), c(3,4,5))` specifies that Group 1 contains variables 1 and 2, Group 2 contains variables 2 and 3, and Group 3 contains variables 3, 4, and 5. Can also be a matrix of 0s and 1s with the number of columns equal to the number of groups and the number of rows equal to the number of variables. A value of 1 in row i and column j indicates that variable i is in group j and 0 indicates that variable i is not in group j.
fused	matrix specifying generalized lasso penalty formulation. Each column corresponds to each variable and each row corresponds to a new penalty term, ie if row 1 has the first entry of 1 and the second entry of -1, then the penalty term lambda.fused * \|beta_1 - beta_2\| will be added. Not available now
family	"gaussian" for least squares problems, "binomial" for binary response
nlambda	The number of lambda values. Default is 100.
lambda	A user-specified sequence of lambda values. Left unspecified, the a sequence of lambda values is automatically computed, ranging uniformly on the log scale over the relevant range of lambda values.
lambda.min.ratio	Smallest value for lambda, as a fraction of lambda.max, the (data derived) entry value (i.e. the smallest value for which all parameter estimates are zero). The default depends on the sample size nobs relative to the number of variables nvars. If `nobs > nvars`, the default is 0.0001, close to zero. If `nobs < nvars`, the default is 0.01. A very small value of `lambda.min.ratio` will lead to a saturated fit in the `nobs < nvars` case.
lambda.fused	tuning parameter for fused (generalized) lasso penalty
alpha	currently not used. Will be used later for fused lasso
group.weights	A vector of values representing multiplicative factors by which each group's penalty is to be multiplied. Often, this is a function (such as the square root) of the number of predictors in each group. The default is to use the square root of group size for the group selection methods.
adaptive.lasso	Flag indicating whether or not to use adaptive lasso weights. If set to `TRUE` and `group.weights` is unspecified, then this will override `group.weights`. If a vector is supplied to group.weights, then the `adaptive.lasso` weights will be multiplied by the `group.weights` vector
adaptive.fused	Flag indicating whether or not to use adaptive fused lasso weights.
penalty.factor	vector of weights to be multiplied to the tuning parameter for the group lasso penalty. A vector of length equal to the number of groups
penalty.factor.fused	vector of weights to be multiplied to the tuning parameter for the fused lasso penalty. A vector of length equal to the number of variables. mostly for internal usage
gamma	power to raise the MLE estimated weights by for the adaptive lasso. defaults to 1
standardize	Logical flag for `x` variable standardization, prior to fitting the models. The coefficients are always returned on the original scale. Default is `standardize = TRUE`. If variables are in the same units already, you might not wish to standardize.
intercept	Should intercept(s) be fitted (`default = TRUE`) or set to zero (`FALSE`)
compute.se	Should standard errors be computed? If `TRUE`, then models are re-fit with no penalization and the standard errors are computed from the refit models. These standard errors are only theoretically valid for the adaptive lasso (when `adaptive.lasso` is set to `TRUE`)
rho	ADMM parameter. must be a strictly positive value. By default, an appropriate value is automatically chosen
dynamic.rho	`TRUE`/`FALSE` indicating whether or not the rho value should be updated throughout the course of the ADMM iterations
maxit	integer. Maximum number of ADMM iterations. Default is 500.
abs.tol	absolute convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is `10^{-5}`, which is typically adequate.
rel.tol	relative convergence tolerance for ADMM iterations for the relative dual and primal residuals. Default is `10^{-5}`, which is typically adequate.
irls.tol	convergence tolerance for IRLS iterations. Only used if `family != "gaussian"`. Default is `10^{-5}`.
irls.maxit	integer. Maximum number of IRLS iterations. Only used if `family != "gaussian"`. Default is 100.

Value

An object with S3 class "oglasso"

Examples

library(vennLasso)

set.seed(123)
n.obs <- 1e3
n.vars <- 50

true.beta <- c(rep(0,2), 1, -1, rep(0, 8), 0.5, -0.5, 1, rep(0, 35))

x <- matrix(rnorm(n.obs * n.vars), n.obs, n.vars)
y <- rnorm(n.obs, sd = 3) + drop(x %*% true.beta)

groups <- c(list(c(1,2), c(2,3), c(3,4,5), 5:10, 6:12, 7:15), lapply(16:50, function(x) x))

if (FALSE) {
fit <- oglasso(x = x, y = y, group = groups)
}