regmest {pense}

Compute (Adaptive) Elastic Net M-Estimates of Regression

Description

Compute elastic net M-estimates along a grid of penalization levels with optional penalty loadings for adaptive elastic net.

Usage

regmest(
  x,
  y,
  alpha,
  nlambda = 50,
  lambda,
  lambda_min_ratio,
  scale,
  starting_points,
  penalty_loadings,
  intercept = TRUE,
  cc = 4.7,
  eps = 1e-06,
  explore_solutions = 10,
  explore_tol = 0.1,
  max_solutions = 10,
  comparison_tol = sqrt(eps),
  sparse = FALSE,
  ncores = 1,
  standardize = TRUE,
  algorithm_opts = mm_algorithm_options(),
  add_zero_based = TRUE,
  mscale_bdp = 0.25,
  mscale_opts = mscale_algorithm_options()
)

Arguments

x

n by p matrix of numeric predictors.

y

vector of response values of length n. For binary classification, y should be a factor with 2 levels.

alpha

elastic net penalty mixing parameter with 0 \le \alpha \le 1. alpha = 1 is the LASSO penalty, and alpha = 0 the Ridge penalty.

nlambda

number of penalization levels.

lambda

optional user-supplied sequence of penalization levels. If given and not NULL, nlambda and lambda_min_ratio are ignored.

lambda_min_ratio

Smallest value of the penalization level as a fraction of the largest level (i.e., the smallest value for which all coefficients are zero). The default depends on the sample size relative to the number of variables and alpha. If more observations than variables are available, the default is 1e-3 * alpha, otherwise 1e-2 * alpha.

scale

fixed scale of the residuals.

starting_points

a list of staring points, created by starting_point(). The starting points are shared among all penalization levels.

penalty_loadings

a vector of positive penalty loadings (a.k.a. weights) for different penalization of each coefficient. Only allowed for alpha > 0.

intercept

include an intercept in the model.

cc

cutoff constant for Tukey's bisquare \rho function.

eps

numerical tolerance.

explore_solutions

number of solutions to compute up to the desired precision eps.

explore_tol

numerical tolerance for exploring possible solutions. Should be (much) looser than eps to be useful.

max_solutions

only retain up to max_solutions unique solutions per penalization level.

comparison_tol

numeric tolerance to determine if two solutions are equal. The comparison is first done on the absolute difference in the value of the objective function at the solution. If this is less than comparison_tol, two solutions are deemed equal if the squared difference of the intercepts is less than comparison_tol and the squared L_2 norm of the difference vector is less than comparison_tol.

sparse

use sparse coefficient vectors.

ncores

number of CPU cores to use in parallel. By default, only one CPU core is used. Not supported on all platforms, in which case a warning is given.

standardize

logical flag to standardize the x variables prior to fitting the M-estimates. Coefficients are always returned on the original scale. This can fail for variables with a large proportion of a single value (e.g., zero-inflated data). In this case, either compute with standardize = FALSE or standardize the data manually.

algorithm_opts

options for the MM algorithm to compute estimates. See mm_algorithm_options() for details.

add_zero_based

also consider the 0-based regularization path in addition to the given starting points.

mscale_bdp, mscale_opts

options for the M-scale estimate used to standardize the predictors (if standardize = TRUE).

Value

a list-like object with the following items

alpha

the sequence of alpha parameters.

lambda

a list of sequences of penalization levels, one per alpha parameter.

scale

the used scale of the residuals.

estimates

a list of estimates. Each estimate contains the following information:

intercept

intercept estimate.

beta

beta (slope) estimate.

lambda

penalization level at which the estimate is computed.

alpha

alpha hyper-parameter at which the estimate is computed.

objf_value

value of the objective function at the solution.

statuscode

if ⁠> 0⁠ the algorithm experienced issues when computing the estimate.

status

optional status message from the algorithm.

call

the original call.

See Also

regmest_cv() for selecting hyper-parameters via cross-validation.

coef.pense_fit() for extracting coefficient estimates.

plot.pense_fit() for plotting the regularization path.

Other functions to compute robust estimates: pense()