Sparse Group Lasso

Efficient implementation of sparse group lasso with optional bound constraints on the coefficients; see . It supports the use of a sparse design matrix as well as returning coefficient estimates in a sparse matrix. Furthermore, it correctly calculates the degrees of freedom to allow for information criteria rather than cross-validation with very large data. Finally, the interface to compiled code avoids unnecessary copies and allows for the use of long integers.

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