# fusedlasso: Fused lasso penalized linear regression In extlasso: Maximum penalized likelihood estimation with extended lasso penalty

## 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

 ```1 2``` ```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 |β| = √(β^2+α) 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

## Author(s)

B N Mandal and Jun Ma

## References

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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")) ```

### Example output

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extlasso documentation built on May 2, 2019, 11:39 a.m.