Shooting Algorithms for the Lasso and Group Lasso
Shooting algorithm implemented in Matlab for solving the Lasso  and group Lasso  problems in the penalized form.
Input: a design matrix X, a response vector Y, grouping index G (only required by group Lasso), penalty parameter lambda.
Output: the estimated coefficient vector.
Lasso and group Lasso for the diabetes data set used in .
lambda = 100;
b = lassoShooting(X, Y, lambda);
% Grouping index:
% G1: age & sex; G2: BMI & BP; G3: S1-S6;
G = [1 1 2 2 3 3 3 3 3 3];
b_grp = grplassoShooting(X, Y, G, lambda);
% We can solve the Lasso and group Lasso on a set of penalty parameters (example below lambda=0:2:730) with the shooting algorithms.
Remark: in general, the group Lasso path is NOT piecewise linear.
 Fu (1998) Penalized regression: the bridge versus the lasso. J. Comput. Graph. Stats.
 Yuan and Lin (2005) Model selection and estimation in regression with grouped variables. JRSSB.
 Efron Brad, et al. (2004) Least angle regression. Annals of Statistics, 32(2):407-499.