lassoshooting {lassoshooting}

Lasso Shooting

Description

Efficient estimates of sparse regression coefficients with a lasso (L1) penalty

Usage

lassoshooting(X=NULL, y=NULL, lambda, XtX=NULL, Xty=NULL, thr=1.0e-6,
              maxit=1e4, nopenalize=NULL, penaltyweight=NULL, trace=0, ...)

Arguments

X

Design matrix: N by p matrix of p explanatory variables

y

vector of 1 response variable for N observations

XtX

X'X, could be given together with X'y instead of X and y

Xty

X'y, could be given together with X'X instead of X and y

lambda

(Non-negative) regularization parameter for lasso. lambda=0 means no regularization.

thr

Threshold for convergence. Default value is 1e-4. Iterations stop when max absolute parameter change is less than thr

maxit

Maximum number of iterations of outer loop. Default 10,000

nopenalize

List of coefficients not to penalize starting at 0

penaltyweight

p weights, one per variable, will be multiplied by overall lambda penalty

trace

Level of detail for printing out information as iterations proceed. Default 0 – no information

...

Reserved for experimental options

Details

Estimates a sparse regression coefficient vector using a lasso (L1) penalty using the approach of cyclic coordinate descent. See references for details.

The solver does NOT include an intercept, add a column of ones to x if your data is not centered.

Value

A list with components

coefficients

Estimated regression coefficient vector

iterations

Number of iterations of outer loop used by algorithm

delta

Change in parameter value at convergence

infnorm

||X'y||_\infty

Author(s)

Tobias Abenius

References

Rebecka Jörnsten, Tobias Abenius, Teresia Kling, Linnéa Schmidt, Erik Johansson, Torbjörn Nordling, Bodil Nordlander, Chris Sander, Peter Gennemark, Keiko Funa, Björn Nilsson, Linda Lindahl, Sven Nelander. (2011) Network modeling of the transcriptional effects of copy number aberrations in glioblastoma. Molecular Systems Biology 7 (to appear)

Friedman J, Hastie T, et al. (2007) Pathwise coordinate optimization. Ann Appl Stat 1: 302–332

Fu WJ (1998) Penalized regressions: the bridge versus the lasso. J Comput Graph Statist 7: 397–416

Examples

  ## Not run: 
set.seed(42)

b <- seq(3,3,length=10)
n<-100;
p<-10; 
X <- matrix(rnorm(n*p),n,p)
noise <- as.matrix(rnorm(n,sd=0.1))
y <- X 

require(lassoshooting)
# FIXME: write proper example using R built in dataset
#add intercept column to the design matrix
Xdesign <- cbind(1,X)
lambda <- 20
#don't penalize the intercept
bhat <- lassoshooting(X=Xdesign,y=y,lambda=lambda,nopenalize=0) 

#above equals below 
bhat1 <- lassoshooting(X=Xdesign,y=y,lambda=2*lambda,penaltyweight=c(0,seq(0.5,0.5,length=p-1)))

T1 <- all(abs(bhat1-bhat) < 1e-20)

c <- 10
bhat2 <- lassoshooting(X=Xdesign,y=y, lambda=lambda, penaltyweight=c(0,1,1,1,1,1,c,c,c,c,c))

T2 <- all(bhat2[2:6] > bhat2[7:11])
T1 && T2
  
## End(Not run)