path.sparsestep: Approximate path algorithm for the SparseStep model

In sparsestep: SparseStep Regression

Description

Fits the entire regularization path for SparseStep using a Golden Section search. Note that this algorithm is approximate, there is no guarantee that the solutions _between_ induced values of lambdas do not differ from those calculated. For instance, if solutions are calculated at λ[i] and λ[i+1], this algorithm ensures that λ[i+1] has one more zero than the solution at λ[i] (provided the recursion depth is large enough). There is however no guarantee that there are no different solutions between λ[i] and λ[i+1]. This is an ongoing research topic.

Note that this path algorithm is not faster than running the sparsestep function with the same λ sequence.

Usage

path.sparsestep(
  x,
  y,
  max.depth = 10,
  gamma0 = 1000,
  gammastop = 1e-04,
  IMsteps = 2,
  gammastep = 2,
  normalize = TRUE,
  intercept = TRUE,
  force.zero = TRUE,
  threshold = 1e-07,
  XX = NULL,
  Xy = NULL,
  use.XX = TRUE,
  use.Xy = TRUE,
  quiet = FALSE
)

Arguments

x	matrix of predictors
y	response
max.depth	maximum recursion depth
gamma0	starting value of the gamma parameter
gammastop	stopping value of the gamma parameter
IMsteps	number of steps of the majorization algorithm to perform for each value of gamma
gammastep	factor to decrease gamma with at each step
normalize	if TRUE, each variable is standardized to have unit L2 norm, otherwise it is left alone.
intercept	if TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included
force.zero	if TRUE, absolute coefficients smaller than the provided threshold value are set to absolute zero as a post-processing step, otherwise no thresholding is performed
threshold	threshold value to use for setting coefficients to absolute zero
XX	The X'X matrix; useful for repeated runs where X'X stays the same
Xy	The X'y matrix; useful for repeated runs where X'y stays the same
use.XX	whether or not to compute X'X and return it
use.Xy	whether or not to compute X'y and return it
quiet	don't print search info while running

Value

A "sparsestep" S3 object is returned, for which print, predict, coef, and plot methods exist. It has the following items:

call	The call that was used to construct the model.
lambda	The value(s) of lambda used to construct the model.
gamma0	The gamma0 value of the model.
gammastop	The gammastop value of the model
IMsteps	The IMsteps value of the model
gammastep	The gammastep value of the model
intercept	Boolean indicating if an intercept was fitted in the model
force.zero	Boolean indicating if a force zero-setting was performed.
threshold	The threshold used for a forced zero-setting
beta	The resulting coefficients stored in a sparse matrix format (dgCMatrix). This matrix has dimensions nvar x nlambda
a0	The intercept vector for each value of gamma of length nlambda
normx	Vector used to normalize the columns of x
meanx	Vector of column means of x
XX	The matrix X'X if use.XX was set to TRUE
Xy	The matrix X'y if use.Xy was set to TRUE

Author(s)

Gerrit J.J. van den Burg, Patrick J.F. Groenen, Andreas Alfons
Maintainer: Gerrit J.J. van den Burg <[e-mail]>

References

Van den Burg, G.J.J., Groenen, P.J.F. and Alfons, A. (2017). SparseStep: Approximating the Counting Norm for Sparse Regularization, arXiv preprint arXiv:1701.06967 [stat.ME]. URL https://arxiv.org/abs/1701.06967.

See Also

coef, print, predict, plot, and sparsestep.

Examples

x <- matrix(rnorm(100*20), 100, 20)
y <- rnorm(100)
pth <- path.sparsestep(x, y)

sparsestep documentation built on Jan. 13, 2021, 9:34 p.m.