Least squares with an L1 penalty, which selects while it shrinks

Ridge shrinks every coefficient and drops none; subset selection drops but does not shrink, and its objective is combinatorial. The L1 penalty is the convex relaxation that does both at once, and the non-differentiable corner at zero is exactly the feature that produces exact zeros rather than merely small numbers.

Usage

Lassrg(y, X, lam, max_iter = 10000, tol = 1e-12)

Arguments

y: Response of length n.
X: Design matrix, n by p.
lam: Penalty, non-negative.
max_iter: Maximum sweeps.
tol: Convergence tolerance.

Value

Whatever Esllso returns, unchanged.

Details

An alias. The solver is Esllso; lassrg is the same method as esllso and it is the same problem solved the same way, so only the argument order differs here.

Formula: min_beta ||y - X beta||^2 + lambda ||beta||_1 – Tibshirani (1996).

References

Tibshirani, R. (1996). Journal of the Royal Statistical Society Series B 58(1):267-288. doi:10.1111/j.2517-6161.1996.tb02080.x .

Examples

Lassrg(y = c(1, 2, 3, 4, 5, 6, 7, 8), X = c(1, 2, 3, 4, 5, 6, 7, 8), lam = 5L)
#> $estimate
#> [1] 0.9754902
#> 
#> $beta
#> [1] 0.9754902
#> 
#> $n_nonzero
#> [1] 1
#> 
#> $active_set
#> [1] 0
#> 
#> $objective
#> [1] 4.938725
#> 
#> $iterations
#> [1] 2
#> 
#> $converged
#> [1] TRUE
#> 
#> $lambda
#> [1] 5
#> 
#> $n
#> [1] 8
#> 
#> $p
#> [1] 1
#> 
#> $method
#> [1] "lasso coordinate descent; constant columns unpenalised; lambda is n x glmnet's"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"