Shooting algorithm implemented in Matlab for solving the Lasso and group Lasso 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.
Example: Lasso and group Lasso for the diabetes data set used in [1].
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.
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| Lasso path |
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| Group Lasso path |
References:
[1] Fu (1998) Penalized regression: the bridge versus the lasso. J. Comput. Graph. Stats.
[2] Yuan and Lin (2005) Model selection and estimation in regression with grouped variables. JRSSB.
[3] Efron et al. (2004) Least angle regression. Annals of Statistics, 32(2):407-499.