L1.ceiling: The largest meaningful value of the L1 parameter

In gelnet: Generalized Elastic Nets

The largest meaningful value of the L1 parameter

Description

Computes the smallest value of the LASSO coefficient L1 that leads to an all-zero weight vector for a given linear regression problem.

Usage

L1.ceiling(
  X,
  y,
  a = rep(1, nrow(X)),
  d = rep(1, ncol(X)),
  P = diag(ncol(X)),
  m = rep(0, ncol(X)),
  l2 = 1,
  balanced = FALSE
)

Arguments

X	n-by-p matrix of n samples in p dimensions
y	n-by-1 vector of response values. Must be numeric vector for regression, factor with 2 levels for binary classification, or NULL for a one-class task.
a	n-by-1 vector of sample weights (regression only)
d	p-by-1 vector of feature weights
P	p-by-p feature association penalty matrix
m	p-by-1 vector of translation coefficients
l2	coefficient for the L2-norm penalty
balanced	boolean specifying whether the balanced model is being trained (binary classification only) (default: FALSE)

Details

The cyclic coordinate descent updates the model weight w_k using a soft threshold operator S( \cdot, \lambda_1 d_k ) that clips the value of the weight to zero, whenever the absolute value of the first argument falls below \lambda_1 d_k. From here, it is straightforward to compute the smallest value of \lambda_1, such that all weights are clipped to zero.

Value

The largest meaningful value of the L1 parameter (i.e., the smallest value that yields a model with all zero weights)

gelnet documentation built on July 22, 2026, 9:07 a.m.