Estimating equation for differentiable LASSO regression

Uses a smooth approximation to the L1 penalty based on the standard normal CDF and PDF.

Usage

ee_dlasso_regression(
  theta,
  X,
  y,
  model,
  penalty,
  s = 1e-06,
  weights = NULL,
  center = 0,
  offset = NULL
)

Arguments

theta

Numeric vector of length p.

X

Numeric n-by-p design matrix.

y

Numeric vector of n observed outcome values.

model

Character string: "linear", "logistic", or "poisson".

penalty

Numeric scalar or vector of length p. Must be non-negative.

s

Numeric smoothing parameter. Must be greater than zero. Default 1e-6.

weights

Optional numeric vector of n weights. Default NULL.

center

Numeric scalar or vector. Default 0.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A p-by-n matrix.

Examples

# A penalty vector gives one value per column of the design matrix. A scalar
# penalty would shrink the intercept along with the slopes. The estimating
# equation carries the penalty's derivative. Here that derivative is smooth,
# so the estimating equation is differentiable and no warning is issued,
# unlike ee_lasso_regression() whose derivative has unbounded slope at the
# penalty center.
fit <- m_estimate(
  mpg ~ wt + hp,
  data = mtcars,
  .ee = ee_dlasso_regression,
  model = "linear",
  penalty = c(0, 5, 5)
)
coef(fit)
#> (Intercept)          wt          hp 
#> 36.68027321 -3.58300419 -0.03451029