extlasso (version 0.3)

fusedlasso: Fused lasso penalized linear regression

Description

The function computes coefficients of a fused lasso penalized linear regression model using modified Jacobi gradient descent Algorithm for a pair of lambda1 and lambda2 values.

Usage

fusedlasso(x,y,lambda1,lambda2,intercept=TRUE,normalize=TRUE, 
alpha=1e-6,eps=1e-6,tol=1e-8,maxiter=1e5)

Arguments

x

x is a matrix of order n x p where n is number of observations and p is number of predictor variables. Rows should represent observations and columns should represent predictor variables.

y

y is a vector of response variable of order n x 1.

lambda1

The value of lambda1

lambda2

The value of lambda2

intercept

If TRUE, model includes intercept, else the model does not have intercept.

normalize

If TRUE, columns of x matrix are normalized with mean 0 and norm 1 prior to fitting the model. The coefficients at end are returned on the original scale. Default is normalize = TRUE.

alpha

The quantity in approximating \(|\beta| = \sqrt(\beta^2+\alpha)\) Default is alpha = 1e-12.

eps

A value which is used to set a coefficient to zero if coefficients value is within - eps to + eps. Default is eps = 1e-6.

tol

Tolerance criteria for convergence of solutions. Default is tol = 1e-6.

maxiter

Maximum number of iterations permissible for solving optimization problem for a particular lambda. Default is 10000. Rarely you need to change this to higher value.

Value

An object of class `extlasso' with following components:

intercept

Value of intercept: TRUE or FALSE as used in input

coef

A vector of order (p+1) if intercept is TRUE, first element being estimates of intercept or a vector of order p if intercept is FALSE. Here p is number of predictor variables.

lambda1

The value of lambda1

lambda2

The value of lambda2

L1norm

L1norm of the coefficients

lambda.iter

Number of iterations

of.value

Objective function value

References

Mandal, B.N. and Jun Ma, (2014). A Jacobi-Armijo Algorithm for LASSO and its Extensions.

Examples

# NOT RUN {
n=50
p=100
rho=0
beta=rep(0,p)
beta[1:20]=1
beta[11:15]=2
beta[25]=3
beta[41:45]=1
x=matrix(rnorm(n*p),n,p)
y=x%*%beta+rnorm(n,0,0.5)
f1<-fusedlasso(x,y,lambda1=0.1,lambda2=1)
plot(beta,col="blue",type="b",pch=1,ylim=range(beta,f1$coef))
lines(f1$coef,type="b",lty=1,col="black")
legend("topright",pch=1,lty=1,merge=TRUE,text.col=c("blue","black"),legend=c("True","Fitted"))
# }