l1.reg: Greedy Coordinate Descent for L1 regression

In CDLasso: Coordinate Descent Algorithms for Lasso Penalized L1, L2, and Logistic Regression

Description

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

Usage

	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 [e-mail]

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

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

Example output

 Call: 
l1.reg.default(x[out$selected, ], y, lambda = 0)
# of cases= 500 
# of predictors= 5 

 Lambda used: 0 


 Intercept: 
[1] 0

 Selected Coefficient Estimates: 
     Predictor Estimate           
[1,] "1"       "1.00000000489118" 
[2,] "2"       "1.00000000020971" 
[3,] "3"       "0.999999996731973"
[4,] "4"       "0.99999999756147" 
[5,] "5"       "0.999999999034168"

 Number of Active Variables: 
[1] 5

CDLasso documentation built on May 1, 2019, 8:02 p.m.