Sparse Group Lasso.

sparsegl

The goal of sparsegl is to fit regularization paths for sparse group-lasso penalized learning problems. The model is typically fit for a sequence of regularization parameters $\lambda$. Such estimators minimize

$$ -\ell(\beta | y,\ \mathbf{X}) + \lambda(1-\alpha)\sum_{g\in G} \lVert\beta_g\rVert_2 + \lambda\alpha \lVert\beta\rVert_1. $$

The main focus of this package is for the case where the loglikelihood corresponds to Gaussian or logistic regression. But we also provide the ability to fit arbitrary GLMs using stats::family() objects. Details may be found in Liang, Cohen, Sólon Heinsfeld, Pestilli, and McDonald (2024).

Installation

You can install the released version of sparsegl from CRAN with:

install.packages("sparsegl")

You can install the development version from GitHub with:

# install.packages("remotes")
remotes::install_github("dajmcdon/sparsegl")

Minimal Example

set.seed(1010)
n <- 100
p <- 200
X <- matrix(data = rnorm(n * p, mean = 0, sd = 1), nrow = n, ncol = p)
eps <- rnorm(n, mean = 0, sd = 1)
beta_star <- c(
  rep(5, 5), c(5, -5, 2, 0, 0),
  rep(-5, 5), c(2, -3, 8, 0, 0), rep(0, (p - 20))
)
y <- X %*% beta_star + eps
groups <- rep(1:(p / 5), each = 5)
fit1 <- sparsegl(X, y, group = groups)
plot(fit1, y_axis = "coef", x_axis = "penalty", add_legend = FALSE)

References