Least absolute shrinkage and selection operator¶

The least absolute shrinkage and selection operator (lasso) solves the problem

$\min_z \frac{1}{2} \| A z - b \|_2^2 + \lambda \| z \|_1,$

where the $$\ell_1$$ penalty coefficient, $$\lambda$$, provides a tradeoff between sparsity and fidelity.

The following routines make use of Alternating Direction Method of Multipliers techniques for finding approximate solutions and are inspired by a simple MATLAB script due to Boyd et al.

C++ API¶

Int Lasso(const Matrix<F> &A, const Matrix<F> &b, Base<F> lambda, Matrix<F> &z, Base<F> rho = 1, Base<F> alpha = 1.2, Int maxIter = 500, Base<F> absTol = 1e-6, Base<F> relTol = 1e-4, bool inv = true, bool progress = true)
Int Lasso(const AbstractDistMatrix<F> &A, const AbstractDistMatrix<F> &b, Base<F> lambda, AbstractDistMatrix<F> &z, Base<F> rho = 1, Base<F> alpha = 1.2, Int maxIter = 500, Base<F> absTol = 1e-6, Base<F> relTol = 1e-4, bool inv = true, bool progress = true)

TODO: Discussion of parameters

C API¶

ElError ElLasso_s(ElConstMatrix_s A, ElConstMatrix_s b, float lambda, ElMatrix_s z, ElInt* numIts)
ElError ElLasso_d(ElConstMatrix_d A, ElConstMatrix_d b, double lambda, ElMatrix_d z, ElInt* numIts)
ElError ElLasso_c(ElConstMatrix_c A, ElConstMatrix_c b, float lambda, ElMatrix_c z, ElInt* numIts)
ElError ElLasso_z(ElConstMatrix_z A, ElConstMatrix_z b, double lambda, ElMatrix_z z, ElInt* numIts)
ElError ElLassoDist_s(ElConstDistMatrix_s A, ElConstDistMatrix_s b, float lambda, ElDistMatrix_s z, ElInt* numIts)
ElError ElLassoDist_d(ElConstDistMatrix_d A, ElConstDistMatrix_d b, double lambda, ElDistMatrix_d z, ElInt* numIts)
ElError ElLassoDist_c(ElConstDistMatrix_c A, ElConstDistMatrix_c b, float lambda, ElDistMatrix_c z, ElInt* numIts)
ElError ElLassoDist_z(ElConstDistMatrix_z A, ElConstDistMatrix_z b, double lambda, ElDistMatrix_z z, ElInt* numIts)