Solving Generalized LASSO with fixed \(\lambda = 1\)

Solves efficiently the generalized LASSO problem of the form $$ \hat{\beta} = \operatorname{argmin} \frac{1}{2} || y - \beta ||_2^2 + ||D\beta||_1 $$ where \(\beta\) and \(y\) are \(m\)-dimensional vectors and \(D\) is a \((c \times m)\)-matrix where \(c \geq m\). We solve this optimization problem using an adaption of the ADMM algorithm presented in Zhu (2017).

Usage

genlassoRcpp(Y, W, m, eta1, eta2, a, rho, max_iter, eps, truncate)

Arguments

Y

The \(y\) vector of length \(m\)

W

The weight matrix \(W\) of dimensions \(m \times m\)

m

The number of graphs

eta1

Equals \(\lambda_1 / rho\)

eta2

Equals \(\lambda_2 / rho\)

a

Value added to the diagonal of \(-D'D\) so that the matrix is positive definite, see matrix_A_inner_ADMM in package CVN

rho

The ADMM's parameter

max_iter

Maximum number of iterations

eps

Stopping criterion. If differences are smaller than \(\epsilon\), algorithm is halted

truncate

Values below truncate are set to 0

Value

The estimated vector \(\hat{\beta}\)

References

Zhu, Y. (2017). An Augmented ADMM Algorithm With Application to the Generalized Lasso Problem. Journal of Computational and Graphical Statistics, 26(1), 195–204. https://doi.org/10.1080/10618600.2015.1114491