Greedy Coordinate Descent for L1 regression

Description

Greedy Coordinate Descent for L1 regression with p predictors and n cases

Usage

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	l1.reg(X, Y, lambda = 1)

Arguments

X

p x n design matrix - Note that the rows of X correspond to predictors and the columns to cases.

Y

Outcome of length n

lambda

Penalization Parameter. To find optimal lambda, use cv.l1.reg.

Details

l1.reg performs a new algorithm for estimating regression coefficients with a lasso penalty. The algorithm is based on greedy coordinate descent and Edgeworth's algorithm for ordinary L1 regression. This L1 algorithm is faster than the cyclic coordinate descent in L2 regression (l2.reg).

Value

X

The design matrix.

Y

The outcome variable for cases.

cases

The number of cases

predictors

The number of predictors

lambda

The value of penalization parameter lambda used.

objective

The value of the objective function

residual

A vector of length p listing the residuals

L1

The sum of the residuals

estimate

The estimate of the coefficients

nonzeros

The name of "selected" variables included in the model.

selected

The name of the "selected" variables included in the model.

Author(s)

Edward Grant, Kenneth Lange, Tong Tong Wu

Maintainer: Edward Grant edward.m.grant@gmail.com

References

Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, Volume 2, No 1, 224-244.

See Also

print.l1.reg

summary.l1.reg

cv.l1.reg

plot.cv.l1.reg

l2.reg

Examples

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set.seed(100)
n=500
p=2000
nz = c(1:5)
true.beta<-rep(0,p)
true.beta[nz] = c(1,1,1,1,1)

x=matrix(rnorm(n*p),p,n)
y = t(x) %*% true.beta

rownames(x)<-1:nrow(x)
colnames(x)<-1:ncol(x)

#Lasso penalized L1 regression
out<-l1.reg(x,y,lambda=50)

#Re-estimate parameters without penalization
out2<-l1.reg(x[out$selected,],y,lambda=0)
out2