olasso function

Error standard deviation estimation using organic lasso

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)

Arguments

• x: An n by p design matrix. Each row is an observation of p features.
• y: A response vector of size n.
• intercept: Indicator of whether intercept should be fitted. Default to be TRUE.
• thresh: Threshold value for underlying optimization algorithm to claim convergence. Default to be 1e-8.

Returns

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.

Examples

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])

See Also

olasso_path, olasso_cv