given the solution path corresponding to γ=0. Note that the
predictor matrix here is the identity, and in this case the new
solution path is given by a simple soft-thresholding operation
(Friedman et al. 2007).
Usage
softthresh(object, lambda, gamma)
Arguments
object
an object of class "fusedlasso", fit with no predictor matrix
X (taken to mean that the predictor matrix is the identity)
and with gamma set to 0. Other objects will issue a warning
that soft-thresholding does not give the exact primal solution path
to a sparsified generalized lasso problem.
lambda
a numeric vector giving the values of lambda at which the solution
should be computed and returned; if missing, defaults to the knots
in the solution path stored in object.
gamma
a numeric variable giving the ratio of the fusion and sparsity
tuning parameters, must be greater than or equal to 0.
Value
Returns a numeric matrix of primal solutions, one column for each
value of lambda.
References
Friedman J., Hastie T., Hoefling H. and Tibshirani, R. (2007),
"Pathwise coordinate optimization", Annals of Applied Statistics
1 (2) 302–332.
See Also
fusedlasso
Examples
# The 1d fused lasso
set.seed(0)
n = 100
beta0 = rep(sample(1:10,5),each=n/5)
beta0 = beta0-mean(beta0)
y = beta0 + rnorm(n,sd=0.8)
a = fusedlasso1d(y)
lambda = 4
b1 = coef(a,lambda=lambda)$beta
gamma = 0.5
b2 = softthresh(a,lambda=lambda,gamma=gamma)
plot(1:n,y)
lines(1:n,b1)
lines(1:n,b2,col="red")
legend("topright",lty=1,col=c("black","red"),
legend=c(expression(gamma==0),expression(gamma==0.5)))