proxGroupSortedL1 {grpSLOPE}

Prox for group SLOPE

Description

Evaluate the proximal mapping for the group SLOPE problem.

Usage

proxGroupSortedL1(y, group, lambda, ...)

Arguments

y

The response vector

group

Either a vector or an object of class groupID (e.g., as produced by getGroupID), which is describing the grouping structure. If it is a vector, then it should contain a group id for each predictor variable.

lambda

A decreasing sequence of regularization parameters \lambda

...

Options passed to prox_sorted_L1

Details

proxGroupSortedL1 evaluates the proximal mapping of the group SLOPE problem by reducing it to the prox for the (regular) SLOPE and then applying the fast prox algorithm for the Sorted L1 norm.

Value

The solution vector.

References

M. Bogdan, E. van den Berg, C. Sabatti, W. Su, E. Candes (2015), SLOPE – Adaptive variable selection via convex optimization, https://arxiv.org/abs/1407.3824

Examples

grp <- c(0,0,0,1,1,0,2,1,0,2)
proxGroupSortedL1(y = 1:10, group = grp, lambda = c(10, 9, 8))
#  [1] 0.2032270 0.4064540 0.6096810 0.8771198 1.0963997 1.2193620 1.3338960
#  [8] 1.7542395 1.8290430 1.9055657