grpSLOPE (version 0.3.3)

lambdaGroupSLOPE: Regularizing sequence for Group SLOPE

Description

Generate the regularizing sequence lambda for the Group SLOPE problem according to one of multiple methods (see Details).

Usage

lambdaGroupSLOPE(method, fdr, group, wt, n.obs = NULL)

Value

A vector containing the calculated lambda values.

Arguments

method

Possible values are "max", "mean", and "corrected". See under Details.

fdr

Target group false discovery rate (gFDR)

group

A vector describing the grouping structure. It should contain a group id for each predictor variable.

wt

A named vector of weights, one weight per group of predictors (named according to names as in vector group)

n.obs

Number of observations (i.e., number of rows in A); required only if method is "corrected"

Details

Multiple methods are available to generate the regularizing sequence lambda:

• "max" -- lambdas as in Theorem 2.5 in Brzyski et. al. (2016). Provalby controls gFDR in orthogonal designs.

• "mean" -- lambdas of equation (2.16) in Brzyski et. al. (2016). Applicable for gFDR control in orthogonal designs. Less conservative than "max".

• "corrected" -- lambdas of Procedure 1 in Brzyski et. al. (2016); in the special case that all group sizes are equal and wt is a constant vector, Procedure 6 of Brzyski et. al. (2016) is applied. Applicable for gFDR control when predictors from different groups are stochastically independent.

References

D. Brzyski, A. Gossmann, W. Su, and M. Bogdan (2016) Group SLOPE -- adaptive selection of groups of predictors, https://arxiv.org/abs/1610.04960

D. Brzyski, A. Gossmann, W. Su, and M. Bogdan (2019) Group SLOPE -- adaptive selection of groups of predictors. Journal of the American Statistical Association 114 (525): 419–33.

Examples

# specify 6 groups of sizes 2, 3, and 4
group <- c(1, 1, 2, 2, 2, 3, 3, 3, 3,
           4, 4, 5, 5, 5, 6, 6, 6, 6)
# set the weight for each group to the square root of the group's size
wt <- rep(c(sqrt(2), sqrt(3), sqrt(4)), 2)
names(wt) <- 1:6
# compute different lambda sequences
lambda.max <- lambdaGroupSLOPE(method="max", fdr=0.1, group=group, wt=wt) 
lambda.mean <- lambdaGroupSLOPE(method="mean", fdr=0.1, group=group, wt=wt) 
lambda.corrected <- lambdaGroupSLOPE(method="corrected", fdr=0.1,
                                     group=group, wt=wt, n.obs=1000)
rbind(lambda.max, lambda.mean, lambda.corrected)
#                      [,1]     [,2]     [,3]     [,4]     [,5]     [,6]
# lambda.max       2.023449 1.844234 1.730818 1.645615 1.576359 1.517427
# lambda.mean      1.880540 1.723559 1.626517 1.554561 1.496603 1.447609
# lambda.corrected 1.880540 1.729811 1.637290 1.568971 1.514028 1.467551