Solving Generalized LASSO with fixed \(\lambda = 1\) Solves efficiently the generalized LASSO problem of the form $$ \hat{\beta} = \text{argmin } \frac{1}{2} || y - \beta ||_2^2 + ||D\beta||_1 $$ 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).
Arguments
- Y
The \(y\) vector of length \(m\)
- W
The weight matrix \(W\) of dimensions \(m x m\)
- 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- 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
truncateare set to0
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