bcd

block coordinate descent for group lasso problems

Description

The bcd package uses block coordinate descent to fit common GLMs with a group lasso penalty. The model fitting implementation is in C++, and the package is used in R with wrapper functions from Rcpp. Run help("fit_bcd") in R for descriptions of the function arguments and for some examples of using the package.

Features:

• tested against glmnet and grpreg
• fits linear, logistic, multinomial, multiresponse Gaussian, and Poisson models
• supports sparse and dense design matrices
• supports multiple group penalization options:
  • sparse group lasso penalization
  • overlapping group lasso penalization
  • models with 1 or more than 1 unpenalized coefficient
  • models with 0 unpenalized coefficients, including models where the intercept is penalized or the model does not contain an intercept
• varying weights for each sample

Installation

Install using devtools package:

devtools::install_github("stephenberg/bcd")

Example

Linear regression with simulated data

library(bcd)
data(exampleData)
fit_linear=fit_bcd(X=X,y=y_gaussian,family="gaussian",groups=grouping,penaltyFactor=penaltyFactor)

Example with overlapping groups

A more complicated logistic regression example with overlapping groups:

data(exampleData)
grouping=list(as.integer(1),2:10,11:30,11:50)
fit_overlap=fit_bcd(X=X,y=y_binary,family="logistic",groups=grouping,penaltyFactor=penaltyFactor)

Comparison to results from glmnet and grpreg

The tests/ folder of the repository contains a substantial collection of test functions for comparing bcd, glmnet, and grpreg under many settings. Below, we show the setting and output for two of the linear regression test examples.

The tests use the example data that comes with the package:

library(bcd)
library(glmnet)
library(grpreg)
data(exampleData)

Testing linear regression vs. grpreg, with 3 groups and an unpenalized intercept:

fitBCD=fit_bcd(X=X,y=y_gaussian,family="gaussian",groups=grouping,penaltyFactor=penaltyFactor)
fitGrpreg=grpreg(X=X[,-1],y=y_gaussian,family="gaussian",group=c(rep(1,9),rep(2,20),rep(3,20)),eps = 10^-16)
betaBCD=matrix(unlist(fitBCD$beta),ncol=length(fitBCD$beta))
max(abs(betaBCD-fitGrpreg$beta))

[1] 4.468648e-15

Testing linear regression vs. glmnet, with lasso (l₁) penalty only

fitBCD=fit_bcd(X=X,y=y_gaussian,family="gaussian",groups=as.list(1:50),penaltyFactor=c(0,rep(1,49)),tol=10^-12)
fitGlmnet=glmnet(x=X[,-1],y=y_gaussian,family="gaussian",lambda=fitBCD$lambda*sqrt(n),thresh=10^-30)
betaBCD=matrix(unlist(fitBCD$beta),ncol=length(fitBCD$beta))
max(abs(betaBCD-coefficients(fitGlmnet)))

[1] 2.250804e-15