olasso {natural} | R Documentation |
Solve the organic lasso problem
\tilde{\sigma}^2_{\lambda} = \min_{\beta} ||y - X \beta||_2^2 / n + 2 \lambda ||\beta||_1^2
with two pre-specified values of tuning parameter:
\lambda_1 = log p / n
, and \lambda_2
, which is a Monte-Carlo estimate of ||X^T e||_\infty^2 / n^2
, where e
is n-dimensional standard normal.
olasso(x, y, intercept = TRUE, thresh = 1e-08)
x |
An |
y |
A response vector of size |
intercept |
Indicator of whether intercept should be fitted. Default to be |
thresh |
Threshold value for underlying optimization algorithm to claim convergence. Default to be |
A list object containing:
n
and p
: The dimension of the problem.
lam_1
, lam_2
: log(p) / n
, and an Monte-Carlo estimate of ||X^T e||_\infty^2 / n^2
, where e
is n-dimensional standard normal.
a0_1
, a0_2
: Estimate of intercept, corresponding to lam_1
and lam_2
.
beta_1
, beta_2
: Organic lasso estimate of regression coefficients, corresponding to lam_1
and lam_2
.
sig_obj_1
, sig_obj_2
: Organic lasso estimate of the error standard deviation, corresponding to lam_1
and lam_2
.
set.seed(123)
sim <- make_sparse_model(n = 50, p = 200, alpha = 0.6, rho = 0.6, snr = 2, nsim = 1)
ol <- olasso(x = sim$x, y = sim$y[, 1])